Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

safia21

  • 3 years ago

− Calculate the length of LM in the isosceles right triangle ∆ KLM

  • This Question is Closed
  1. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1 Attachment
  2. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You can use the pythagorean theorem since it has a right angle. Are you familiar with it?

  3. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no im kinda confused

  4. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    do you know what a hypotenuse is?

  5. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  6. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so the pythagorean theorem is: \[ a^2 + b^2 = c^2 \] where c is the hypotenuse. since this is an isosceles triangle, a = b, don't you think?

  7. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  8. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so can you take it form here? since a = b, \( a^2 + a^2 = c^2 \)

  9. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is a and what is like what do you plug in

  10. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    well let me ask, what is a hypotenuse?

  11. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the longset side of a right triangle

  12. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    very good! which is the side *directly* across from the right angle. so the other two sides would be 'a' and 'b', but this triangle is isosceles so a = b. therefore a is an unknown that we want to solve for and 'c' is the length of the hypotenuse

  13. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so if we have \(a^2 + a^2 = c^2\) where \( c = 36 \) we only have 1 unknown so we should be able to solve this like a regular algebra problem.

  14. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  15. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    are you still confused? all that's left is to simplify this equation and solve.

  16. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay i got 36?

  17. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    show me your steps. i don't that's right.

  18. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    think*

  19. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what is \( a^2 + a^2 \) ?

  20. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    (@victor, please consider that the best way for a person to learn something is to have the person discover it on their own rather than just giving that person an answer.)

  21. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes i need the steps!

  22. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    there's no reason you can't do it yourself, though. you have an equation. where are you getting stuck? show me your work and i can help you.

  23. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    can we start from the beginning im soo sorry!

  24. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    the pythagorean theorem states that (for a right triangle): \[ a^2 + b^2 = c^2\]where c is the hypotenuse. we have the hypotenuse in this case, as you pointed out, and it equals 36, agree?

  25. Victor_Hugo
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It's an isosceles triangle so it has two equal sides and therefor two equal angles. If you add the inner angles of any triangle the result will be 180º. You already know 1 angle = 90º. 180-90=90 And since the two other angles are equal you have 90/2=45. Now that you have all the angles you can use trigonometry and achieve the value of the sides. I recommend you use "sin" or "tan" (as expressed on a calculator).

  26. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  27. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    but this is an isosceles triangle, so the two remaining sides are equal in length, would you agree?

  28. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  29. Victor_Hugo
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Of course, you only need the value of one side.

  30. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so since the two remaining sides are \(a\) and \(b\), we know that \(a =b \) therefore we can simplify the equation to this: \( a^2 + a^2 = c^2 \)

  31. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay and c2 is 36 right so a2+a2= 36^2

  32. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    exactly! so what does \( a^2 + a^2\) equal? we can reduce this to one term.

  33. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a^3

  34. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    not quite. how about this, what does \( x + x \) equal?

  35. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what if i wrote it this way: \( 1x+ 1x \)

  36. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2x^2?

  37. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that wouldn't work. think about if x = 2, 1x + 1x = 1(2) + 1(2) = 4, but 2x^2 = 2(2)^2 = 8 so those two expressions are not equal. when you add terms of the same variable, you just add their "coefficients," the number in front of the variable.

  38. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    o okay

  39. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so what is x + x?

  40. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4

  41. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no x is a variable, not a number. x can be *any* number

  42. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay x^2

  43. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no just add the numbers *in front* of the variable. x = 1x

  44. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2x

  45. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    right! so now let's look at the original equation, what is \( a^2 + a^2 \)

  46. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    keep in mind that \(a^2 \) is the same thing as \(1a^2\)

  47. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2x^4

  48. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    there are no x's in this equation. that was just as an aside example. the question here is to simplify \(a^2 + a^2\) you know that \( x + x = 2x\), so use that same *idea* and apply it to the other equation.

  49. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2a^4

  50. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you don't add the exponents, just the coefficients. \( x = 1x = x^1 = 1x^1 \) are all the same same

  51. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2a^2

  52. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    isnt it a2=B2

  53. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    very good! so let's look at our original equation: \(a^2 + a^2 = 36^2 \) = \(2a^2 = 36^2\)

  54. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes it is, that's how we eliminated the b^2 and replaced it with another a^2

  55. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  56. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so now our equation is \(2a^2 = 36^2\) do you know how to solve algebra problems? that's all this is.

  57. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so i multiply 36 times 36 and divide it by 2

  58. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    absolutely!

  59. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that would be represented like so: \(a^2 = \frac{36^2}{2} \) then you just take the square root of both sides to get 'a' = something

  60. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    a^2 = 36^2 / 2

  61. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    36 right

  62. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    not quite, remember, it's: 36 * 36 / 2

  63. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  64. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    first do 36 * 36, then divide that answer by 2

  65. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    648

  66. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    very good! so we're left with: \( a^2 = 648\) just take the square root of both sides and you have your answer!

  67. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i got 26

  68. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but thats not one of the anwsers

  69. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what are the answers?

  70. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a) 18 b) 18√2 c) 36 d) 36√2

  71. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    well one of those answers roughly equals the number you got.

  72. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    b

  73. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that's right! congrats :)

  74. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks soo much!

  75. heisenberg
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no problem :) i'm glad you wanted to learn rather than just want the answer. it'll always work out better that way. trust me ;)

  76. safia21
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    haha thanks! :)

  77. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.