mathsurgently needed
posted by Anonymous on .
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.

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