smurfy14
  • smurfy14
Word problem help! (File attached)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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smurfy14
  • smurfy14
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anonymous
  • anonymous
do you know the law of cosines?
smurfy14
  • smurfy14
no

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smurfy14
  • smurfy14
we learned it like 2 yrs ago but i forgot
anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
*of sides
smurfy14
  • smurfy14
ok so what is the angle measure?
anonymous
  • anonymous
you have to find it with law of cosines, I got about 126.9 degrees
smurfy14
  • smurfy14
law of cosines? how do you find that? with ur calc?
anonymous
  • anonymous
\[c^2=a^2+b^2-2abcos(\theta)\] c=20 a=7 b=15 solve for theta. You can use a calculator
smurfy14
  • smurfy14
dont have a calc on me but ok what do you do after you get 126.9?
anonymous
  • anonymous
you can find its compliment by taking 180-126.9=53.1
anonymous
  • anonymous
Now you have a right triangle of hypotenuse 15 and angle 53.1 right?
anonymous
  • anonymous
and the leg opposite the angle is your height
anonymous
  • anonymous
so 15*sin(53.1)=h h=12
anonymous
  • anonymous
i got 20
anonymous
  • anonymous
but i am probably wrong again
anonymous
  • anonymous
it cant be that big the hypotenuse is 15
smurfy14
  • smurfy14
ok thanks rsvitale!
anonymous
  • anonymous
yw
smurfy14
  • smurfy14
oh where do i put the angle 53.1? like if i were drawing a pic of it
smurfy14
  • smurfy14
does 53.1 go on the green or red dot?
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anonymous
  • anonymous
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
anonymous
  • anonymous
we used law of cosines to find the angle opposite side of length 20
smurfy14
  • smurfy14
so the one diagnol to the the height of the building? ok
anonymous
  • anonymous
yep the one opposite the height of the building is 53.1
anonymous
  • anonymous
oh there's a much easier way to do this too. do you want to know the simpler way?
anonymous
  • anonymous
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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