Question

The angle of elevation from a ball on a football field to the top of a 30-foot tall goal post is 16°42'. How far is the football from the base of the goal post? a) 61.2 feet b) 30.0 feet c) 34.1 feet d) 72.8 feet

Answer 1

Using tangent function with the given angle of elevation and the height of the goal post, we solve for the adjacent side, which is the distance from the football to the base of the goal post, and find that it is approximately 101.1 feet.

Step-by-step explanation:

To solve for the distance from the football to the base of the goal post, we can use trigonometry, specifically the tangent function, which relates angles to opposite and adjacent sides in a right triangle. Given that the angle of elevation is 16°42' and the height of the goal post is 30 feet, we can set up the following equation using the tangent:

tangent(angle of elevation) = opposite side/adjacent side,

or tan(16°42') = 30/adjacent side.

This can be rearranged to find the adjacent side (which in this case is the distance from the football to the base of the goal post):

adjacent side = 30/tan(16°42').

Using a calculator to find tan(16°42') and solving for the adjacent side, we find that the distance is approximately 101.1 feet. Since this value is not listed as one of the choices, it suggests there may have been a misunderstanding in the question data or typo. However, the method to find the distance remains valid.