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Emily778

  • 3 years ago

Find the value of each variable. If your answer is not an integar, express it in simplest radical form.

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  1. Emily778
    • 3 years ago
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    |dw:1362695099329:dw|

  2. Emily778
    • 3 years ago
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    I need to know step by step on how to solve this.

  3. Emily778
    • 3 years ago
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    @jim_thompson5910 Please help. :(

  4. jim_thompson5910
    • 3 years ago
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    is this a right triangle?

  5. Emily778
    • 3 years ago
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    |dw:1362695278150:dw|

  6. jim_thompson5910
    • 3 years ago
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    ok thank you

  7. jim_thompson5910
    • 3 years ago
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    |dw:1362695556789:dw|

  8. jim_thompson5910
    • 3 years ago
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    this is because all angles must add to 180 notice how 45 + 45 + 90 = 180

  9. jim_thompson5910
    • 3 years ago
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    so we have a 45-45-90 triangle which means that the two legs are congruent

  10. jim_thompson5910
    • 3 years ago
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    |dw:1362695629297:dw|

  11. jim_thompson5910
    • 3 years ago
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    if the leg is x, then the hypotenuse is x*sqrt(2) So hypotenuse = x*sqrt(2) hypotenuse = sqrt(2)*sqrt(2) hypotenuse = (sqrt(2))^2 hypotenuse = 2

  12. jim_thompson5910
    • 3 years ago
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    |dw:1362695698593:dw|

  13. Emily778
    • 3 years ago
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    if you already figured out the hypotenuse's are the same, why'd you do all that work up there?

  14. jim_thompson5910
    • 3 years ago
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    the legs are the same, not the hypotenuses

  15. Emily778
    • 3 years ago
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    oh. Should I put down the equations you did to get a decent grade?

  16. jim_thompson5910
    • 3 years ago
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    and I did all that work based on the fact that if you have a 45-45-90 triangle, then you'll have this basic template |dw:1362695974272:dw|

  17. jim_thompson5910
    • 3 years ago
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    also, if you know the legs, you can find the hypotenuse using the pythagorean theorem, which is a^2 + b^2 = c^2

  18. Emily778
    • 3 years ago
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    you're kinda confusing me. Like, I'm understanding it more, but the way you're explaining it. You're just kind of throwing it out randomly. I need a step by step procedure.

  19. jim_thompson5910
    • 3 years ago
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    alright, did you see how I figured out how x = sqrt(2) ?

  20. jim_thompson5910
    • 3 years ago
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    the legs of a 45-45-90 triangle are congruent x is a leg and so is the sqrt(2) length, so that means x = sqrt(2)

  21. jim_thompson5910
    • 3 years ago
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    with me so far?

  22. Emily778
    • 3 years ago
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    can you write it down, like.."step 1, step 2" to make it more simple?

  23. jim_thompson5910
    • 3 years ago
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    the legs of a 45-45-90 triangle are congruent so x must be sqrt(2) units long since the other leg is sqrt(2) units long this means x = sqrt(2) --------------------------------------------- we know both legs are sqrt(2) units, so let's use them to find the hypotenuse y a^2 + b^2 = c^2 ( sqrt(2) )^2 + ( sqrt(2) )^2 = y^2 2 + 2 = y^2 4 = y^2 y^2 = 4 y = sqrt( 4 ) y = 2 So the hypotenuse is 2 units

  24. jim_thompson5910
    • 3 years ago
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    |dw:1362696451678:dw|

  25. Emily778
    • 3 years ago
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    would I write that down on a paper?

  26. jim_thompson5910
    • 3 years ago
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    yeah if you wanted to, you could also use the template above as a shortcut

  27. jim_thompson5910
    • 3 years ago
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    this template |dw:1362696580301:dw|

  28. Emily778
    • 3 years ago
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    Ugh..I'll show you what I have on my paper and you say if it's correct or not..

  29. jim_thompson5910
    • 3 years ago
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    ok

  30. Emily778
    • 3 years ago
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    |dw:1362696649159:dw|

  31. jim_thompson5910
    • 3 years ago
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    ok good so far, you just have shown that the missing angle is 45 degrees

  32. jim_thompson5910
    • 3 years ago
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    oh and you threw in x = sqrt(2)

  33. jim_thompson5910
    • 3 years ago
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    I would say why x is sqrt(2) and you can say that the legs are congruent (because it's a 45-45-90 triangle)

  34. Emily778
    • 3 years ago
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    okay

  35. jim_thompson5910
    • 3 years ago
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    the next thing you need to show is how to get y

  36. jim_thompson5910
    • 3 years ago
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    there are 2 ways to do it: use the template above or the pythagorean theorem

  37. jim_thompson5910
    • 3 years ago
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    both ways are shown in this post

  38. Emily778
    • 3 years ago
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    can you show them again. you can copy them

  39. jim_thompson5910
    • 3 years ago
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    here is the pythagorean theorem method

  40. jim_thompson5910
    • 3 years ago
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    the legs of a 45-45-90 triangle are congruent so x must be sqrt(2) units long since the other leg is sqrt(2) units long this means x = sqrt(2) --------------------------------------------- we know both legs are sqrt(2) units, so let's use them to find the hypotenuse y a^2 + b^2 = c^2 ( sqrt(2) )^2 + ( sqrt(2) )^2 = y^2 2 + 2 = y^2 4 = y^2 y^2 = 4 y = sqrt( 4 ) y = 2 So the hypotenuse is 2 units

  41. jim_thompson5910
    • 3 years ago
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    sound good?

  42. Emily778
    • 3 years ago
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    Yeah. Sorry, I was off the computer. Taking a break. :P

  43. Emily778
    • 3 years ago
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    Wait..Y=2? @jim_thompson5910

  44. jim_thompson5910
    • 3 years ago
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    yes, y = 2

  45. jim_thompson5910
    • 3 years ago
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    |dw:1362701799670:dw|

  46. Emily778
    • 3 years ago
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    could I make it look like this?|dw:1362701962485:dw|

  47. Emily778
    • 3 years ago
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    from the one thing you showed me? instead of putting down "sqrt"?

  48. Emily778
    • 3 years ago
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    @jim_thompson5910

  49. jim_thompson5910
    • 3 years ago
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    yes you could do it that way (it's a bit cleaner looking)

  50. Emily778
    • 3 years ago
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    just a question.. How does it equal y?

  51. jim_thompson5910
    • 3 years ago
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    what do you mean?

  52. Emily778
    • 3 years ago
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    nevermind I think I understand.

  53. jim_thompson5910
    • 3 years ago
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    are you sure?

  54. jim_thompson5910
    • 3 years ago
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    alright, I'm glad it's (sorta) making sense

  55. Emily778
    • 3 years ago
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    so, x= sqrt2? It can't be simplified?

  56. jim_thompson5910
    • 3 years ago
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    no it cannot

  57. jim_thompson5910
    • 3 years ago
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    that's as simple as it gets for x

  58. Emily778
    • 3 years ago
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    okay, can you help me with 2 more? Or no?

  59. jim_thompson5910
    • 3 years ago
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    sure I can help

  60. jim_thompson5910
    • 3 years ago
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    what's your question

  61. Emily778
    • 3 years ago
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    the second one explains the same thing, but the problem is different.

  62. Emily778
    • 3 years ago
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    I'll draw it

  63. jim_thompson5910
    • 3 years ago
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    alright

  64. Emily778
    • 3 years ago
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    |dw:1362702888077:dw|

  65. Emily778
    • 3 years ago
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    :/

  66. jim_thompson5910
    • 3 years ago
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    the legs are equal (we have another 45-45-90 triangle)

  67. jim_thompson5910
    • 3 years ago
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    so y = x

  68. Emily778
    • 3 years ago
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    would I write down that y=x?

  69. jim_thompson5910
    • 3 years ago
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    use the pythagorean theorem to get |dw:1362703031520:dw|

  70. jim_thompson5910
    • 3 years ago
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    then you plug in y = x |dw:1362703073963:dw|

  71. jim_thompson5910
    • 3 years ago
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    and you solve for x

  72. Emily778
    • 3 years ago
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    is that " X^2 + X^2"?

  73. Emily778
    • 3 years ago
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    where did the y go?

  74. jim_thompson5910
    • 3 years ago
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    y = x so y and x are the same

  75. Emily778
    • 3 years ago
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    ohh. I get ya. How do I solve for X for this?

  76. jim_thompson5910
    • 3 years ago
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    so you can replace y with x

  77. Emily778
    • 3 years ago
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    How do i solve for x?

  78. jim_thompson5910
    • 3 years ago
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    well the two x^2 terms add up to 2x^2

  79. jim_thompson5910
    • 3 years ago
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    so you will have 2x^2 = 450 then what?

  80. Emily778
    • 3 years ago
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    well, I'd think you'd divide the 450 by 2 but it's squared..so, I don't know..

  81. jim_thompson5910
    • 3 years ago
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    yes, 2x^2 = 450 x^2 = 450/2 x^2 = 225 x = sqrt(225) x = 15

  82. jim_thompson5910
    • 3 years ago
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    so both x and y are 15 (since y = x)

  83. Emily778
    • 3 years ago
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    Oh, I get it. Thankyou. :)

  84. Emily778
    • 3 years ago
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    here's the 3rd one..

  85. jim_thompson5910
    • 3 years ago
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    yw

  86. Emily778
    • 3 years ago
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    |dw:1362704401057:dw|

  87. jim_thompson5910
    • 3 years ago
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    this is another 45-45-90 triangle (the legs are congruent)

  88. Emily778
    • 3 years ago
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    Okay

  89. jim_thompson5910
    • 3 years ago
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    so what does that mean for the value of y?

  90. Emily778
    • 3 years ago
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    it's bigger

  91. jim_thompson5910
    • 3 years ago
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    yes and what else

  92. jim_thompson5910
    • 3 years ago
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    how can you find the value of y?

  93. Emily778
    • 3 years ago
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    isn't it a^2 +b^2=c^2?

  94. jim_thompson5910
    • 3 years ago
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    very good

  95. jim_thompson5910
    • 3 years ago
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    replace a with sqrt(5) replace b with sqrt(5) and you want to solve for c

  96. Emily778
    • 3 years ago
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    I know. :)

  97. jim_thompson5910
    • 3 years ago
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    ok great

  98. Emily778
    • 3 years ago
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    Do I actually solve sqrt5^2 + sqrt5^2 in the calculator?

  99. jim_thompson5910
    • 3 years ago
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    well the square of the square roots cancel each other out

  100. jim_thompson5910
    • 3 years ago
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    so (sqrt(5))^2 = 5

  101. jim_thompson5910
    • 3 years ago
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    so you are left with 5 + 5 which turns into 10

  102. jim_thompson5910
    • 3 years ago
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    so c^2 = 10

  103. Emily778
    • 3 years ago
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    I'm confused. How did you get 5+5?

  104. jim_thompson5910
    • 3 years ago
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    |dw:1362706218096:dw|

  105. jim_thompson5910
    • 3 years ago
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    so that's how I got 2 five terms being added

  106. Emily778
    • 3 years ago
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    wouldn't I replace C with Y?

  107. jim_thompson5910
    • 3 years ago
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    you would

  108. jim_thompson5910
    • 3 years ago
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    so y^2 = 10

  109. jim_thompson5910
    • 3 years ago
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    making |dw:1362706377944:dw|

  110. Emily778
    • 3 years ago
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    is that it for that problem?

  111. Emily778
    • 3 years ago
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    @jim_thompson5910

  112. jim_thompson5910
    • 3 years ago
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    yes, you found y, so you're done

  113. Emily778
    • 3 years ago
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    Oh, I'm so sorry. but I don't get this other one. Can you help me with it? c:

  114. jim_thompson5910
    • 3 years ago
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    sure

  115. Emily778
    • 3 years ago
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    |dw:1362707591687:dw|

  116. Emily778
    • 3 years ago
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    @jim_thompson5910

  117. Emily778
    • 3 years ago
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    hullo?

  118. jim_thompson5910
    • 3 years ago
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    sry was afk for a sec

  119. jim_thompson5910
    • 3 years ago
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    were you able to get anywhere with this at all?

  120. Emily778
    • 3 years ago
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    No. :/

  121. Emily778
    • 3 years ago
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    I think Y = 2 sqrt 3?

  122. Emily778
    • 3 years ago
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    @jim_thompson5910

  123. jim_thompson5910
    • 3 years ago
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    sry i had to go afk, but I'm back

  124. jim_thompson5910
    • 3 years ago
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    y is actually 2 the legs are not congruent

  125. jim_thompson5910
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    x = 2*y x = 2*2 x =4

  126. jim_thompson5910
    • 3 years ago
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    the reason how I know y is 2 is from this template |dw:1362709753724:dw|

  127. Emily778
    • 3 years ago
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    um, 60 degrees is down below and down below, its 2 sqrt3

  128. Emily778
    • 3 years ago
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    @jim_thompson5910

  129. jim_thompson5910
    • 3 years ago
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    well i flipped the triangle around, but if it were oriented the way the problem has it, then you would have |dw:1362710229246:dw|

  130. Emily778
    • 3 years ago
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    |dw:1362710294844:dw|

  131. Emily778
    • 3 years ago
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    you missed the 3?

  132. Emily778
    • 3 years ago
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    I mean 2

  133. jim_thompson5910
    • 3 years ago
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    the 2*sqrt(3) is above though isnt it?

  134. Emily778
    • 3 years ago
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    I just showed you the diagram. :P

  135. jim_thompson5910
    • 3 years ago
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    but in this one, the 2*sqrt(3) is above |dw:1362710579138:dw|

  136. Emily778
    • 3 years ago
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    Are you supposed to change what I showed you?

  137. jim_thompson5910
    • 3 years ago
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    no i just copied what you drew

  138. Emily778
    • 3 years ago
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    you're mixing up everything I just drew and you know that. ._.

  139. Emily778
    • 3 years ago
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    look up at the picture again..

  140. jim_thompson5910
    • 3 years ago
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    yeah i see the new one, but you drew a totally different one

  141. jim_thompson5910
    • 3 years ago
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    or is it a case the second one is the correct one and the first one was a typo?

  142. Emily778
    • 3 years ago
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    OH I'm sorry!

  143. jim_thompson5910
    • 3 years ago
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    yeah i was like...what in the world lol

  144. Emily778
    • 3 years ago
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    that was my fault.

  145. jim_thompson5910
    • 3 years ago
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    its fine, so which one is it?

  146. Emily778
    • 3 years ago
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    the second one is correct.

  147. jim_thompson5910
    • 3 years ago
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    ok one sec

  148. Emily778
    • 3 years ago
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    k

  149. Emily778
    • 3 years ago
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    are you gonna help? I don't have all day.

  150. jim_thompson5910
    • 3 years ago
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    |dw:1362712584316:dw|

  151. jim_thompson5910
    • 3 years ago
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    the value of x is exactly half that of the hypotenuse

  152. Emily778
    • 3 years ago
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    That's correct. xP Lol.

  153. jim_thompson5910
    • 3 years ago
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    yeah just wanted to make sure and put it up again

  154. jim_thompson5910
    • 3 years ago
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    so x = 2*sqrt(3)/2 = sqrt(3)

  155. jim_thompson5910
    • 3 years ago
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    which means |dw:1362712746325:dw|

  156. Emily778
    • 3 years ago
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    wait stop

  157. jim_thompson5910
    • 3 years ago
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    ok whats up

  158. Emily778
    • 3 years ago
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    is it 2 times sqrt 3/2?

  159. jim_thompson5910
    • 3 years ago
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    yes

  160. jim_thompson5910
    • 3 years ago
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    the 2 terms cancel

  161. Emily778
    • 3 years ago
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    so I write this down? x = 2*sqrt(3)/2 = sqrt(3)

  162. jim_thompson5910
    • 3 years ago
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    yes and that will give you the value of x

  163. Emily778
    • 3 years ago
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    Just to make sure we're on the same topic..|dw:1362713238955:dw|

  164. jim_thompson5910
    • 3 years ago
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    yep

  165. Emily778
    • 3 years ago
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    is that how it should be shown?

  166. jim_thompson5910
    • 3 years ago
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    yes you have it correct, so now that you have x, you can find y

  167. jim_thompson5910
    • 3 years ago
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    y = x*sqrt(3) y = sqrt(3)*sqrt(3) y = 3

  168. Emily778
    • 3 years ago
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    so, Y= 3 and X= Sqrt 3

  169. Emily778
    • 3 years ago
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    ?

  170. jim_thompson5910
    • 3 years ago
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    yes good

  171. Emily778
    • 3 years ago
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    wanna help me with one more please? :D

  172. jim_thompson5910
    • 3 years ago
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    ok one more

  173. Emily778
    • 3 years ago
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    :) Thanks!

  174. jim_thompson5910
    • 3 years ago
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    sure thing

  175. Emily778
    • 3 years ago
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    |dw:1362714107413:dw|

  176. jim_thompson5910
    • 3 years ago
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    |dw:1362714258167:dw|

  177. jim_thompson5910
    • 3 years ago
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    x = 2*12 x = 24 since the hypotenuse is double the shorter leg in a 30-60-90 triangle

  178. jim_thompson5910
    • 3 years ago
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    y = 12*sqrt(3) because of the template given above

  179. Emily778
    • 3 years ago
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    where'd you get the 2 in the first one?

  180. jim_thompson5910
    • 3 years ago
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    in general, with any 30-60-90 triangle the hypotenuse is twice as long as the shorter leg

  181. Emily778
    • 3 years ago
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    oh, so that's why it's 2 x 24..Okay,

  182. jim_thompson5910
    • 3 years ago
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    2 * 12 = 24, but yeah you have it

  183. Emily778
    • 3 years ago
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    what's Y?

  184. jim_thompson5910
    • 3 years ago
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    y = 12*sqrt(3)

  185. jim_thompson5910
    • 3 years ago
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    sry mixed up the 30 and the 60

  186. jim_thompson5910
    • 3 years ago
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    |dw:1362714824453:dw|

  187. Emily778
    • 3 years ago
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    What is the answer for Y? I got 20..:/

  188. jim_thompson5910
    • 3 years ago
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    20 is incorect

  189. jim_thompson5910
    • 3 years ago
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    incorrect*

  190. jim_thompson5910
    • 3 years ago
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    |dw:1362714907609:dw|

  191. Emily778
    • 3 years ago
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    you can't simplify it?

  192. jim_thompson5910
    • 3 years ago
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    no

  193. jim_thompson5910
    • 3 years ago
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    that's as simplified as it gets

  194. Emily778
    • 3 years ago
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    how did you find y?

  195. jim_thompson5910
    • 3 years ago
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    in the template above, do you see how the longer leg is x*sqrt(3) ?

  196. Emily778
    • 3 years ago
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    ohhh.. now I get it.

  197. Emily778
    • 3 years ago
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    Thankyou ! :)

  198. jim_thompson5910
    • 3 years ago
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    ok I would write that template down, it's very handy

  199. jim_thompson5910
    • 3 years ago
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    also the 45-45-90 template as well

  200. Emily778
    • 3 years ago
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    thankyou for helping me

  201. jim_thompson5910
    • 3 years ago
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    you're welcome, sry for being afk a lot lol

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