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Emily778

  • 3 years ago

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

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  1. Emily778
    • 3 years ago
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    |dw:1362774575688:dw|

  2. jim_thompson5910
    • 3 years ago
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    is that a 9? or a 4?

  3. Emily778
    • 3 years ago
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    9

  4. jim_thompson5910
    • 3 years ago
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    ok thanks

  5. jim_thompson5910
    • 3 years ago
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    here's the template again |dw:1362774782473:dw| I would add this to your notes if you don't have it already

  6. jim_thompson5910
    • 3 years ago
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    notice how the number in front of the sqrt(3) on the longer leg is 9 so that must mean that x = 9

  7. Emily778
    • 3 years ago
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    how did you get 30 and 2x?

  8. jim_thompson5910
    • 3 years ago
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    well the given angle is 60, which adds to the right angle 90 to get 90+60 = 150 the remaining angle must be 30 in order for the three to add to 180

  9. jim_thompson5910
    • 3 years ago
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    since 150 + 30 = 180

  10. jim_thompson5910
    • 3 years ago
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    as for the 2x... the hypotenuse is always twice as long as the shorter leg in a 30-60-90 triangle

  11. jim_thompson5910
    • 3 years ago
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    so that explains the x for the shorter leg and 2x for the hypotenuse

  12. Emily778
    • 3 years ago
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    should I write that process down?

  13. jim_thompson5910
    • 3 years ago
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    yes I would if you're not familiar with it

  14. Emily778
    • 3 years ago
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    would it be a good idea to write it on my homework?

  15. jim_thompson5910
    • 3 years ago
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    if you want to, there's nothing wrong with using this template

  16. jim_thompson5910
    • 3 years ago
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    you can draw the template off to the side and show that x must be 9

  17. jim_thompson5910
    • 3 years ago
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    when you match up the terms

  18. Emily778
    • 3 years ago
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    why did you get rid of the 9?

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

  20. Emily778
    • 3 years ago
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    it was 9 sqrt 3? now, it's X sqrt 3?

  21. jim_thompson5910
    • 3 years ago
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    no, I said x was 9 so x = 9

  22. jim_thompson5910
    • 3 years ago
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    oh i see what you mean

  23. Emily778
    • 3 years ago
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    you said in the picture above..

  24. jim_thompson5910
    • 3 years ago
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    9 * sqrt(3) ... what we're given x * sqrt(3)... template

  25. jim_thompson5910
    • 3 years ago
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    notice how the x and the 9 match up

  26. Emily778
    • 3 years ago
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    oh.

  27. jim_thompson5910
    • 3 years ago
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    so that's how I got that x = 9

  28. jim_thompson5910
    • 3 years ago
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    the y and the 2x match up, so y = 2x y = 2*9 y = 18

  29. Emily778
    • 3 years ago
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    you are so confusing me. Can you write it out like, step 1, step 2. And start from the beginning cause I'm lost

  30. jim_thompson5910
    • 3 years ago
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    did you see how I got x = 9?

  31. jim_thompson5910
    • 3 years ago
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    here is your triangle (on top) and the general template triangle (on bottom) |dw:1362776258556:dw|

  32. jim_thompson5910
    • 3 years ago
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    notice how these two sides match up |dw:1362776369974:dw|

  33. Emily778
    • 3 years ago
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    can we not use the template? it's confusing

  34. jim_thompson5910
    • 3 years ago
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    have you learned trig yet?

  35. Emily778
    • 3 years ago
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    can you just show me the process of how to solve this?

  36. jim_thompson5910
    • 3 years ago
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    I'm just curious because if you have, then we can use that

  37. Emily778
    • 3 years ago
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    I just wanna solve it..

  38. jim_thompson5910
    • 3 years ago
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    I know, but I need to know if you know trig so it will make sense if I use it

  39. jim_thompson5910
    • 3 years ago
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    have you learned things like sine, cosine, tangent, etc?

  40. Emily778
    • 3 years ago
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    I think

  41. jim_thompson5910
    • 3 years ago
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    so you've seen things like sine = opposite/hypotenuse ?

  42. jim_thompson5910
    • 3 years ago
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    I'll assume yes

  43. jim_thompson5910
    • 3 years ago
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    tan(30) = opposite/adjacent tan(30) = x/(9*sqrt(3)) sqrt(3)/3 = x/(9*sqrt(3)) ... use a calculator or the unit circle here sqrt(3)*9*sqrt(3) = 3x 9*sqrt(3)*sqrt(3) = 3x 9*3 = 3x 27 = 3x 3x = 27 x = 27/3 x = 9 so you can see that we get the same answer as we did before

  44. jim_thompson5910
    • 3 years ago
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    sure this method is a bit more complicated, but it works it all hinges on whether you know trig or not

  45. Emily778
    • 3 years ago
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    do I write that down?

  46. jim_thompson5910
    • 3 years ago
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    yeah, or you could skip a few steps I guess

  47. jim_thompson5910
    • 3 years ago
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    wherever you see a 'sqrt', use the square root symbol of course

  48. Emily778
    • 3 years ago
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    Should I write this down and skip all the other steps? :) sqrt(3)*9*sqrt(3) = 3x 9*sqrt(3)*sqrt(3) = 3x 9*3 = 3x 27 = 3x 3x = 27 x = 27/3 x = 9

  49. jim_thompson5910
    • 3 years ago
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    I would have the previous steps in there, these ones tan(30) = opposite/adjacent tan(30) = x/(9*sqrt(3)) sqrt(3)/3 = x/(9*sqrt(3)) ------------------------------------------------------- I guess you could skip step 2 to get just these steps tan(30) = opposite/adjacent sqrt(3)/3 = x/(9*sqrt(3))

  50. Emily778
    • 3 years ago
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    I'm confused. Is this 3 times 9? sqrt(3)*9*sqrt(3) = 3x

  51. jim_thompson5910
    • 3 years ago
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    yeah it's just a complicated way of saying 9*3

  52. Emily778
    • 3 years ago
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    so it's actually 9 times 3 sqrt 3= 3x

  53. jim_thompson5910
    • 3 years ago
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    no the sqrt(3) terms multiply to 3 so that's why 9*sqrt(3)*sqrt(3) = 3x turns into 9*3 = 3x

  54. Emily778
    • 3 years ago
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    I got the x. What's the Y?

  55. Emily778
    • 3 years ago
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    @jim_thompson5910

  56. jim_thompson5910
    • 3 years ago
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    well y = 2x so y = 2*9 = 18

  57. jim_thompson5910
    • 3 years ago
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    so y = 18

  58. jim_thompson5910
    • 3 years ago
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    you can use the pythagorean theorem to confirm, but you'd get the same answer (just in a more complicated way)

  59. Emily778
    • 3 years ago
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    how did you find that Y= 2x?

  60. jim_thompson5910
    • 3 years ago
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    well you would use the template...but just remembered you don't like that template very much

  61. jim_thompson5910
    • 3 years ago
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    so you can use a^2 + b^2 = c^2 to find the value of y

  62. jim_thompson5910
    • 3 years ago
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    a^2 + b^2 = c^2 9^2 + (9*sqrt(3))^2 = y^2 81 + 243 = y^2 keep going to solve for y

  63. Emily778
    • 3 years ago
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    y=18?

  64. jim_thompson5910
    • 3 years ago
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    yes good

  65. Emily778
    • 3 years ago
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    okay, 2nd problem! :p

  66. Emily778
    • 3 years ago
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    Recreation. A skateboarding ramp is 12 inches high and rises at an angle of 17 degrees. How long is the base of the ramp? Round to the nearest inch.

  67. Emily778
    • 3 years ago
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    @jim_thompson5910

  68. jim_thompson5910
    • 3 years ago
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    |dw:1362781717017:dw|

  69. jim_thompson5910
    • 3 years ago
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    tan(17) = 12/x x*tan(17) = 12 x = 12/tan(17) x = ???

  70. Emily778
    • 3 years ago
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    do you not know X?

  71. Emily778
    • 3 years ago
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    @jim_thompson5910

  72. jim_thompson5910
    • 3 years ago
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    not until you solve for it

  73. jim_thompson5910
    • 3 years ago
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    by typing 12/tan(17) into the calculator

  74. Emily778
    • 3 years ago
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    oh lol

  75. jim_thompson5910
    • 3 years ago
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    yeah it's not too bad to find

  76. Emily778
    • 3 years ago
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    39.25

  77. jim_thompson5910
    • 3 years ago
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    yep

  78. Emily778
    • 3 years ago
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    so, that's the answer?

  79. jim_thompson5910
    • 3 years ago
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    yes it is

  80. Emily778
    • 3 years ago
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    Last question. I was wrong btw. There's only 3 questions left, not 4. :P

  81. jim_thompson5910
    • 3 years ago
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    ok works for us lol

  82. Emily778
    • 3 years ago
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    The lengths of the diagonals of a rhombus are in 2 inches and 5 inches. Find the measures of the angles of the rhombus to the nearest degree.

  83. jim_thompson5910
    • 3 years ago
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    |dw:1362782836744:dw|

  84. jim_thompson5910
    • 3 years ago
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    |dw:1362782951298:dw|

  85. jim_thompson5910
    • 3 years ago
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    we get this triangle |dw:1362782979724:dw|

  86. jim_thompson5910
    • 3 years ago
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    let x and y be the two unknown angles |dw:1362783041003:dw|

  87. jim_thompson5910
    • 3 years ago
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    tan(x) = 1/2.5 tan(x) = 0.4 x = arctan(0.4) x = ??

  88. Emily778
    • 3 years ago
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    do I draw all of these?

  89. jim_thompson5910
    • 3 years ago
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    you don't have to, but it helps to see how to get the answer

  90. Emily778
    • 3 years ago
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    okay

  91. jim_thompson5910
    • 3 years ago
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    so what do you get for x?

  92. Emily778
    • 3 years ago
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    wait, what's arctan?

  93. jim_thompson5910
    • 3 years ago
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    it's the inverse of tangent

  94. jim_thompson5910
    • 3 years ago
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    if you don't have a calculator that can handle arctan, then look here http://www.google.com/search?hl=&q=arctan%280.4%29+in+degrees&sourceid=navclient-ff&rlz=1B3GGLL_enUS420US420&ie=UTF-8

  95. Emily778
    • 3 years ago
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    how do I get it on my calculator?

  96. jim_thompson5910
    • 3 years ago
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    at the top, you'll see that " arctan(0.4) = 21.8014095 degrees"

  97. jim_thompson5910
    • 3 years ago
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    if you have a TI-83, 85, 86, etc you can hit 2nd, then tan to get arctan

  98. Emily778
    • 3 years ago
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    where's arc on the calculator?

  99. jim_thompson5910
    • 3 years ago
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    what kind of calculator do you have?

  100. Emily778
    • 3 years ago
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    it said "Atan" when i did that, not arctan

  101. Emily778
    • 3 years ago
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    But I still got the right answer

  102. jim_thompson5910
    • 3 years ago
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    oh same thing

  103. jim_thompson5910
    • 3 years ago
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    atan is just a shorter version of arctan

  104. Emily778
    • 3 years ago
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    thankyou. :-)

  105. jim_thompson5910
    • 3 years ago
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    np what did you get for x?

  106. Emily778
    • 3 years ago
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    21.8

  107. Emily778
    • 3 years ago
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    btw, do I find Y?

  108. jim_thompson5910
    • 3 years ago
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    y = 90 - x y = 90 - 21.8 y = 68.2

  109. jim_thompson5910
    • 3 years ago
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    now that you know x and y, you would double them to find the angles of the rhombus

  110. jim_thompson5910
    • 3 years ago
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    21.8*2 = 43.6 which is the measure of one set of angles of the rhombus 68.2*2 = 136.4 which is the measure of another set of angles of the rhombus

  111. Emily778
    • 3 years ago
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    Add X and Y?

  112. jim_thompson5910
    • 3 years ago
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    what do you mean

  113. Emily778
    • 3 years ago
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    oh..double them seperately.

  114. jim_thompson5910
    • 3 years ago
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    yes

  115. jim_thompson5910
    • 3 years ago
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    because we want the angles of the rhombus, not the triangle

  116. Emily778
    • 3 years ago
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    okay, what do I do after?

  117. jim_thompson5910
    • 3 years ago
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    you're done, you found the angles of the rhombus

  118. Emily778
    • 3 years ago
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    oh, so x= 43.6 and y=136.4?

  119. jim_thompson5910
    • 3 years ago
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    no those are the two angles of a rhombus

  120. jim_thompson5910
    • 3 years ago
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    the other two are congruent to those two

  121. jim_thompson5910
    • 3 years ago
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    we have something like this |dw:1362784125897:dw|

  122. Emily778
    • 3 years ago
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    should I draw that?

  123. jim_thompson5910
    • 3 years ago
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    the diagonals are 5 and 2, I just didn't have enough room to draw them in

  124. jim_thompson5910
    • 3 years ago
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    no, they just want the angles

  125. jim_thompson5910
    • 3 years ago
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    you can if you want

  126. Emily778
    • 3 years ago
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    where are the diagonals?

  127. jim_thompson5910
    • 3 years ago
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    lol like i said, i didn't have enough room

  128. jim_thompson5910
    • 3 years ago
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    |dw:1362784257953:dw| see how things get cut off?

  129. Emily778
    • 3 years ago
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    yeah

  130. Emily778
    • 3 years ago
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    so, I'm done now?

  131. jim_thompson5910
    • 3 years ago
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    yes pretty much

  132. Emily778
    • 3 years ago
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    :D YAYAYAYAYAY

  133. jim_thompson5910
    • 3 years ago
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    lol

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