A 20-foot ladder leans against a vertical wall and makes a 68° angle with the ground. How high up the wall does the ladder reach? Round to the nearest tenth of a foot.
Solution
Problem
A 20-foot ladder leans against a vertical wall and makes a 68° angle with the ground. How high up the wall does the ladder reach? Round to the nearest tenth of a foot.
The wall, ground, and ladder form a right triangle.
The ladder is the hypotenuse because it is opposite the 90° angle.
Relative to the 68° angle at the ground, the height up the wall is the opposite side.
We know the opposite side and hypotenuse are related by sine:
sin(θ) = opposite / hypotenuse
Let h represent the height reached by the ladder.
Substitute the known values:
sin(68°) = h / 20
Multiply both sides by 20:
h = 20sin(68°)
Using a calculator in degree mode:
sin(68°) ≈ 0.9272
Therefore:
h ≈ 20(0.9272)
h ≈ 18.544
Round to the nearest tenth:
h ≈ 18.5 feet
Therefore, the ladder reaches approximately 18.5 feet up the wall.
Result
Approximately 18.5 feet