Question

Word problem help! (File attached)

Answer 1

do you know the law of cosines?

Answer 2

no

Answer 3

we learned it like 2 yrs ago but i forgot

Answer 4

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.

Answer 5

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.

Answer 6

*of sides

Answer 7

ok so what is the angle measure?

Answer 8

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

Answer 9

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

Answer 10

\[c^2=a^2+b^2-2abcos(\theta)\]

c=20
a=7
b=15
solve for theta. You can use a calculator

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

and the leg opposite the angle is your height

Answer 15

so 15*sin(53.1)=h

h=12

Answer 16

i got 20

Answer 17

but i am probably wrong again

Answer 18

it cant be that big the hypotenuse is 15

Answer 19

ok thanks rsvitale!

Answer 20

yw

Answer 21

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

Answer 22

does 53.1 go on the green or red dot?

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

yep the one opposite the height of the building is 53.1

Answer 27

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

Answer 28

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