Word problem help! (File attached)

- smurfy14

Word problem help! (File attached)

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- smurfy14

##### 1 Attachment

- anonymous

do you know the law of cosines?

- smurfy14

no

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- smurfy14

we learned it like 2 yrs ago but i forgot

- 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

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

*of sides

- smurfy14

ok so what is the angle measure?

- anonymous

you have to find it with law of cosines, I got about 126.9 degrees

- smurfy14

law of cosines? how do you find that? with ur calc?

- anonymous

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

- smurfy14

dont have a calc on me but ok what do you do after you get 126.9?

- anonymous

you can find its compliment by taking 180-126.9=53.1

- anonymous

Now you have a right triangle of hypotenuse 15 and angle 53.1 right?

- anonymous

and the leg opposite the angle is your height

- anonymous

so 15*sin(53.1)=h
h=12

- anonymous

i got 20

- anonymous

but i am probably wrong again

- anonymous

it cant be that big the hypotenuse is 15

- smurfy14

ok thanks rsvitale!

- anonymous

yw

- smurfy14

oh where do i put the angle 53.1? like if i were drawing a pic of it

- smurfy14

does 53.1 go on the green or red dot?

##### 1 Attachment

- 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

we used law of cosines to find the angle opposite side of length 20

- smurfy14

so the one diagnol to the the height of the building? ok

- anonymous

yep the one opposite the height of the building is 53.1

- anonymous

oh there's a much easier way to do this too. do you want to know the simpler way?

- 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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