To find the height of the hill, we can use the tangent function. The equation for tangent is:
tan(theta) = opposite / adjacent
In this case, theta represents the angle of elevation to the bottom of the tree, A, which is 37°, and the opposite side is the height of the tree, 110 ft. The adjacent side is the height (h) of the hill.
Therefore, we can set up the following equation:
tan(37°) = 110 ft / h
To solve for h, we can rearrange the equation as follows:
h = 110 ft / tan(37°)
Now we can calculate the value of h by plugging in the numbers:
h = 110 ft / tan(37°)
h ≈ 110 ft / 0.7536
h ≈ 146.03 ft
Therefore, the height of the hill is approximately 146.03 feet.