To find the angle of elevation, we can use the definition of sine in a right triangle. The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse.
In this scenario:
- The height of the rock feature above the base of the mountain is the opposite side, which is 200 feet.
- The diagonal distance from your position to the rock feature is the hypotenuse, which is 850 feet.
- The angle of elevation \( \theta \) is what we are trying to find.
We can set up the equation using the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{200}{850} \]
Now, we can calculate \( \frac{200}{850} \):
\[ \frac{200}{850} = \frac{2}{8.5} \approx 0.2353 \]
Next, we use the inverse sine function (arcsin) to find the angle \( \theta \):
\[ \theta = \arcsin(0.2353) \]
Using a calculator to compute this:
\[ \theta \approx 13.5^\circ \]
Rounding to the nearest whole degree gives:
\[ \theta \approx 14^\circ \]
Thus, the angle of elevation is approximately \( \boxed{14} \) degrees.
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