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.(1 point)
feet

Answer 1

To find the distance from the base of the ladder to the house, we can use the cosine function from trigonometry.

In a right triangle formed by the ladder, the house, and the ground:

- The length of the ladder is the hypotenuse (which is 12 feet).
- The angle with the ground is 68 degrees.
- The distance from the base of the ladder to the house is the adjacent side.

The cosine function is defined as:

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

Rearranging the equation gives us:

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

Plugging in the values we have:

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

Now, using a calculator to find \(\cos(68^\circ)\):

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

Now calculate the distance:

\[
\text{adjacent} = 12 \times 0.3746 \approx 4.4952
\]

Rounding this to the nearest tenth gives:

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

Thus, the base of the ladder is approximately **4.5 feet** from the house.