A ladder 20 feet long leans against a building, forming an angle of 71° with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?

Solution:

From the above figure, AC represents the ladder, AB represents the height of the ladder leaning on the wall, BC is the distance of the foot of the ladder from the wall.

From the right angled triangle ABC, we have,

sin 71° = AB/AC

AB = AC × sin 71°

AB = 20 × 0.9455

AB = 18.91 feet

A ladder 20 feet long leans against a building, forming an angle of 71° with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?

Summary: 

A ladder 20 feet long leans against a building, forming an angle of 71° with the level ground. To the nearest foot, the ladder touches 18.91 feet high up the wall of the building.