Word problem help! (File attached)

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Word problem help! (File attached)

Mathematics
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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.

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do you know the law of cosines?
no

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