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smurfy14

  • 5 years ago

Word problem help! (File attached)

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  1. smurfy14
    • 5 years ago
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  2. anonymous
    • 5 years ago
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    do you know the law of cosines?

  3. smurfy14
    • 5 years ago
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    no

  4. smurfy14
    • 5 years ago
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    we learned it like 2 yrs ago but i forgot

  5. anonymous
    • 5 years ago
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    ok I'll tell you: c^2=a^2+b^2-2*a*b*cos(C) for a triangle ABC, c is the side across from C, a across from A, b across from B. C inside of cosine is the angle C.

  6. anonymous
    • 5 years ago
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    you have a triangle if sides 20, 15, 7. use the law of cosines to find the angle where sides of length 7 and 15 meet. Then you subtract that from 180 to find complimentary angle. Now you have an angle and hypotenuse of a right triangle so you can find the height of the ladders.

  7. anonymous
    • 5 years ago
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    *of sides

  8. smurfy14
    • 5 years ago
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    ok so what is the angle measure?

  9. anonymous
    • 5 years ago
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    you have to find it with law of cosines, I got about 126.9 degrees

  10. smurfy14
    • 5 years ago
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    law of cosines? how do you find that? with ur calc?

  11. anonymous
    • 5 years ago
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    \[c^2=a^2+b^2-2abcos(\theta)\] c=20 a=7 b=15 solve for theta. You can use a calculator

  12. smurfy14
    • 5 years ago
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    dont have a calc on me but ok what do you do after you get 126.9?

  13. anonymous
    • 5 years ago
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    you can find its compliment by taking 180-126.9=53.1

  14. anonymous
    • 5 years ago
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    Now you have a right triangle of hypotenuse 15 and angle 53.1 right?

  15. anonymous
    • 5 years ago
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    and the leg opposite the angle is your height

  16. anonymous
    • 5 years ago
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    so 15*sin(53.1)=h h=12

  17. anonymous
    • 5 years ago
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    i got 20

  18. anonymous
    • 5 years ago
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    but i am probably wrong again

  19. anonymous
    • 5 years ago
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    it cant be that big the hypotenuse is 15

  20. smurfy14
    • 5 years ago
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    ok thanks rsvitale!

  21. anonymous
    • 5 years ago
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    yw

  22. smurfy14
    • 5 years ago
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    oh where do i put the angle 53.1? like if i were drawing a pic of it

  23. smurfy14
    • 5 years ago
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    does 53.1 go on the green or red dot?

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  24. anonymous
    • 5 years ago
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    neither those arent the angles I was talking about. slide both of those dots down along the side of length 15. the red one would then be 53.1

  25. anonymous
    • 5 years ago
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    we used law of cosines to find the angle opposite side of length 20

  26. smurfy14
    • 5 years ago
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    so the one diagnol to the the height of the building? ok

  27. anonymous
    • 5 years ago
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    yep the one opposite the height of the building is 53.1

  28. anonymous
    • 5 years ago
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    oh there's a much easier way to do this too. do you want to know the simpler way?

  29. anonymous
    • 5 years ago
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    well i'll just post it here and hopefully you see it. call the distance from the bottom of the 15 length ladder to the base of the wall x, and the height h. There are two right triangles now. One of sides 20,7+x,h and one of sides 15,x,h. By pythagorean theorem: 20^2=h^2+(x+7)^2 15^2=h^2+x^2 solve for h^2 in both equations and set them equal. h^2=20^2-(x+7)^2=15^2-x^2 400-x^2-14x-49=225-x^2 126=14x x=9 so pluging back in to the 15 hypotenuse triangle equation we get h=12

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