Question

A boat is heading towards a lighthouse, whose beacon-light is 104 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 11degrees

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, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22degrees
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Answer 1

The figure is omitted--please sketch it to confirm my answer.

Set your calculator to degree mode.

tan(11°) = 104/x

x = 104/tan(11°)

tan(22°) = 104/y

y = 104/tan(22°)

x - y = (104/tan(11°)) - (104/tan(22°))

= about 228 feet