Question

An extension ladder leans agintst a biulding, making a 75 degree angle of elevation with the ground. The base of the ladder is 8 ft from the base of the building.
To the nearest tenth of a foot, how long is the ladder?

Answer 1

Use soh-cah-toa so for this problem use soh which would be sin75=8/x
sin75= .9659
multiply both sides by x and divide both sides by .9659
you end up with the equation x=8/.9659
 and you get about
x=8.3ft

Answer 2

For this problem, you're going to need to use trig. More specifically, you need to use the tangent function:

tan (value) = opposite/adjacent

tan 75 = opposite/8 (Here, the opposite side is the length of the ladder)

8 * tan 75 = opposite

29.8564065 = opposite

So, the ladder is 29.9 feet.