Question

A boat is sailing about 400 feet from the cliff at the shore of a lake. A sailor on the boat uses a device to measure the angle of elevation between the lake level and the top of the cliff. He draws a diagram like the one below. Using his measurements, find the height of the cliff to the nearest thousandth.

Answer 1

Note that tan 15 deg = h / (400 ft)

tan 15 deg = 0.2679, so (400 ft)(0.2679) = 107 ft

The height of the cliff is approx 107 ft. I don't think it reasonable to try to specify the height to the nearest thousandth of a foot.