From the top of a cliff 150m high, the angles of depression of two boats are 60 and 30. Find the distance between the boats if they are on the opposite sides of the cliff.

Answer 1

tan60 = Y/X1 = 150/X1.
X1 = 150/tan60 = 86.6 m. = Dist. from
1st boat to bottom of cliff.

tan30 = Y/X2 = 150/X2.
X2 = 150/tan30 = 259.8 m. = Dist. from 2nd boat to bottom of cliff.

X = X1 + X2 = 86.6 + 259.8 = 346.4 m. = Dist. between the two boats.