Question

A roofer props a ladder against a wall so that the base of the ladder is 4 feet away from the building. If the angle of elevation from the bottom of the ladder to the roof is 63°, how long is the ladder?

9.22 feet

8.81 feet

10 feet

12.4 feet

Answer 1

To determine the length of the ladder, we can use trigonometric functions. We will use the cosine function, which relates the adjacent side (the distance from the wall to the base of the ladder) to the hypotenuse (the length of the ladder).

Given:
- Distance from the wall (adjacent side) = 4 feet
- Angle of elevation = 63°

Using the cosine function:
\[
\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

This means we can express the length of the ladder (hypotenuse) as:
\[
\text{length of the ladder} = \frac{\text{adjacent}}{\cos(\text{angle})}
\]

Substituting the values:
\[
\text{length of the ladder} = \frac{4}{\cos(63^\circ)}
\]

Calculating \(\cos(63^\circ)\):
\[
\cos(63^\circ) \approx 0.4540
\]

Now substitute this value into the equation:
\[
\text{length of the ladder} = \frac{4}{0.4540} \approx 8.81 \text{ feet}
\]

Thus, the length of the ladder is approximately **8.81 feet**.