To find out how high up the wall the ladder reaches, we can use trigonometry. Specifically, we can use the sine of the angle between the ladder and the ground.
Given:
- Length of the ladder (hypotenuse) = 15 feet
- Angle with the ground = 60°
We want to find the height (opposite side) represented by the equation:
\[ \text{height} = \text{length} \times \sin(\theta) \]
Where:
- \(\theta\) is the angle (\(60^\circ\))
- Length is the length of the ladder (15 feet)
Now, plug in the values:
\[ \text{height} = 15 \times \sin(60^\circ) \]
We know that \(\sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866\).
So, calculate the height:
\[ \text{height} = 15 \times 0.866 \approx 12.99 \text{ feet} \]
Thus, the ladder reaches approximately 12.99 feet up the wall. The correct response is 12.99 feet.