Final answer:
To find the height of the hill, we use the tangent function and the given angle of elevation (22 degrees) and the distance on sight (150 meters). The calculation results in a height of approximately 60.6 meters, with the closest answer choice being 60 meters.
Step-by-step explanation:
The student is looking to find the height of a hill using the distance on sight and the angle of elevation. This is a classic trigonometry problem that involves using the tangent function, which relates the angle of elevation to the opposite side (height of the hill) and the adjacent side (distance on sight).
To find the height of the hill, we use the formula height = distance × tan(angle). Plugging the values given:
- Distance on sight = 150 meters
- Angle of elevation = 22 degrees
We calculate the height as follows:
height = 150 meters × tan(22 degrees)
height ≈ 150 meters × 0.4040 (using a calculator)
height ≈ 60.6 meters
Since the question provides options, the closest one is C. 60 meters.