How high up the wall of the building does a 20-foot ladder touch when it leans against the building at a 71-degree angle?

To find out how high the ladder reaches on the wall, we can use trigonometry. Specifically, we can apply the sine function, which relates the angle of a right triangle to the ratio of the opposite side (height) to the hypotenuse (length of the ladder).

The formula we can use is:

Height = Ladder Length × sin(Angle)

In this case:

• Ladder Length = 20 feet
• Angle = 71 degrees

Now, let’s calculate it:

Height = 20 × sin(71°)

Using a calculator, we find that sin(71°) is approximately 0.9455.

So:

Height ≈ 20 × 0.9455 ≈ 18.91 feet

Rounding to the nearest foot, the ladder touches the building at a height of 19 feet.