Question

A ladder is leaning up against a 70-foot wall at an angle of elevation of 38°. How far is the foot of the ladder from the wall? Round your answer to the nearest tenth of a foot.

Answer 1

The ladder, floor and wall form a straight triangle. The angle between floor and wall is obviously 90, between floor and ladder is 38 (given), so the angle between wall and ladder must be (180-90-38 = 52).

The law of sines says that the side length divided by the sine of the opposite corner is a constant for all three corners.

Let's say the floor length is f.

Then 70/sin(38) = f/sin(52), so f = 70*sin(52)/sin(38) ≈ 89.6.