Question

Ammerah 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? Round to the nearest tenth.

Answer 1

To find the distance from the base of the ladder to the house, we can use the cosine function from trigonometry. The cosine of an angle in a right triangle relates the adjacent side to the hypotenuse.

In this scenario:

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

We can set up the equation using the cosine function:

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

Plugging in the known values:

\[
\cos(68^\circ) = \frac{\text{distance from the house}}{12}
\]

Rearranging the equation to find the distance from the house yields:

\[
\text{distance from the house} = 12 \cdot \cos(68^\circ)
\]

Now, we can calculate \( \cos(68^\circ) \):

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

Now substituting this value back into the equation:

\[
\text{distance from the house} = 12 \cdot 0.3746 \approx 4.4952 \text{ feet}
\]

Rounding to the nearest tenth:

\[
\text{distance from the house} \approx 4.5 \text{ feet}
\]

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