Question

The angle of elevation from a ball on a football field to the top of a 30-foot y'all goal post is 16 degrees 42'. How far is the football from the base of the goal post? Round to the nearest tenth of a foot.

Answer 1

Answer:

  100.0 feet

Step-by-step explanation:

For an acute angle in a right triangle, the cotangent function is the ratio of the adjacent side to the opposite side:

  cot(16°42') = (distance to goal)/(30 ft)

Multiplying by the denominator, we have ...

  (distance to goal) = (30 ft)cot(16°42') = (30 ft)(3.33317) ≈ 100.0 ft

The football is 100.0 feet from the base of the goal.

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cot(16°42') = tan(73.3°)