To find the angle of elevation formed at the base of the ladder, we can use the sine function.
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse. In this case:
- The opposite side is the height the ladder reaches on the wall (17 feet).
- The hypotenuse is the length of the ladder (23 feet).
We can set up the following equation using the sine function: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{17}{23} \]
To find the angle \( \theta \), we can use the inverse sine function: \[ \theta = \arcsin\left(\frac{17}{23}\right) \]
Calculating this: \[ \frac{17}{23} \approx 0.7391 \] Now, we find the arcsin of that value: \[ \theta \approx \arcsin(0.7391) \approx 47.2^\circ \]
Rounding to the nearest whole degree: \[ \theta \approx 47^\circ \]
Thus, the angle of elevation formed where the base of the ladder rests on the ground is approximately 47 degrees.