To find the angle of elevation to the rock feature, we can use the trigonometric relationship involving the sine function. The angle of elevation \( \theta \) can be calculated using the following formula:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case, the "opposite" side is the height of the rock feature above the base of the mountain (200 feet), and the "hypotenuse" is the diagonal distance to the rock feature (850 feet). Thus, we can write:
\[ \sin(\theta) = \frac{200}{850} \]
Now, calculate \( \frac{200}{850} \):
\[ \frac{200}{850} = \frac{20}{85} \approx 0.2353 \]
Next, we need to find \( \theta \). We do this by taking the inverse sine (arcsin) of \( 0.2353 \):
\[ \theta = \arcsin(0.2353) \]
Using a calculator, we find \( \theta \):
\[ \theta \approx 13.5 \]
Rounding to the nearest whole degree gives us:
\[ \theta \approx 14^\circ \]
Therefore, the angle of elevation you are using to look up at the rock feature is approximately 14 degrees.