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.