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.