Final answer:
The height of the hill is approximately 334.88 feet, calculated by using the tangent function of the angle of elevation, which is 15°, with the length of the road being 1250 feet.
Step-by-step explanation:
To find the height of the hill, we can use trigonometry. The road to the top of the hill forms the hypotenuse of a right-angled triangle, while the height we need to find is the opposite side, and the angle given is the angle of elevation.
Using the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle, we get:
tangent(angle) = opposite/adjacent
Given that the angle of elevation is 15° and the length of the road, which is the hypotenuse is 1250 feet, we can set up the equation:
tangent(15°) = height/1250
We rearrange the equation to solve for the height:
height = tangent(15°) × 1250
Calculating this:
height = 0.2679 × 1250
height = 334.875 feet
Therefore, the height of the hill is approximately 334.88 feet.