Question

Ameerah is placing a 12-foot ladder against the house. The ladder makes a 68-degree angle with the ground. How far is the base of the ladder from the house? Enter your response as a decimal. Round to the nearest tenth.

___ feet

Answer 1

To find the distance from the base of the ladder to the house, we can use the cosine function in a right triangle, where:

- The ladder is the hypotenuse (12 feet).
- The angle between the ground and the ladder is 68 degrees.
- The distance from the base of the ladder to the house is the adjacent side of the triangle.

The cosine function relates the adjacent side to the hypotenuse:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Substituting in the known values:

\[
\cos(68^\circ) = \frac{\text{adjacent}}{12}
\]

To find the adjacent side (the distance from the base of the ladder to the house), we rearrange the equation:

\[
\text{adjacent} = 12 \cdot \cos(68^\circ)
\]

We can calculate \(\cos(68^\circ)\) using a calculator:

\[
\cos(68^\circ) \approx 0.3746
\]

Now we plug this value into our equation:

\[
\text{adjacent} \approx 12 \cdot 0.3746 \approx 4.4952
\]

Rounding this to the nearest tenth:

\[
\text{adjacent} \approx 4.5
\]

Thus, the distance from the base of the ladder to the house is approximately:

\[
\boxed{4.5} \text{ feet}
\]