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

x+y

tan 30 = x/150
x = 150 tan 30

tan 60 = y/150
y 150 tan 60
so
d = 150 (tan 30 + tan 60)
d = 150 (1/sqrt 3 + sqrt 3 /2)
= 150 (2 + 3)/2sqrt 3
= 375/sqrt 3
= 216.5