Question

Rashaad leans a 22-foot ladder against a wall so that it forms an angle of 65degrees ∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

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

Given:
- Length of the ladder (hypotenuse) = 22 feet
- Angle with the ground = 65 degrees

The height \( h \) that the ladder reaches on the wall can be calculated using the sine function as follows:

\[
\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In this case, the "opposite" side is the height \( h \) we want to find, and the "hypotenuse" is the length of the ladder:

\[
\sin(65^\circ) = \frac{h}{22}
\]

Now, we can solve for \( h \):

\[
h = 22 \cdot \sin(65^\circ)
\]

Next, we need to calculate \( \sin(65^\circ) \). Using a calculator:

\[
\sin(65^\circ) \approx 0.9063
\]

Now plug this value back into the equation:

\[
h = 22 \cdot 0.9063 \approx 19.96
\]

So, rounding to the nearest hundredth, the height that the ladder reaches on the wall is approximately:

\[
\boxed{19.96}
\] feet.