Question

A boat is heading towards a lighthouse, whose beacon-light is 110 feet above the

water. From point A, the boat's crew measures the angle of elevation to the beacon,
16°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 21°. Find the distance from point A to point B.
Round your answer to the nearest foot if necessary.

Answer 1

Answer: 97

Explanation:

`\tan 16^(\circ)=(110)/(x+y) \\ \\ \implies (x+y)/(110)=(1)/(\tan 16^(\circ)) \\ \\ \implies x+y=(110)/(\tan 16^(\circ)) \\ \\ \\ \\ \tan 21^(\circ)=(110)/(x) \\ \\ \implies (x)/(110)=(1)/(\tan 21^(\circ)) \\ \\ \implies x=(110)/(\tan 21^(\circ)) \\ \\ \\ \\ \therefore (110)/(\tan 21^(\circ))+y=(110)/(\tan 16^(\circ)) \\ \\ y=(110)/(\tan 16^(\circ))-(110)/(\tan 21^(\circ)) \\ \\ y \approx 97`