Question

A ladder leans against a wall in such a way that the base of the ladder is 9 feet from the wall and the top of the ladder reaches a point of 12 feet off the side of the wall.

a. find the exact length of the ladder.

b. find the cosine of the angle of the ladder makes with the ground.

Answer 1

a. 15 ft

b. cos(53.13) = 0.6

Explanation:

a. use pythagorean theorem to find hypotenuse.

9^2 + 12^2 = x^2

225 = x^2

15 = x

b. find the angle that the ladder makes with the ground first.

sin^-1(12/15) = 53.13 degrees

find the cosine of that angle

cos(53.13) = 0.6