Question

An observer in a lighthouse 48.8 m above sea level saw two vessels moving directly towards the lighthouse. He observed that the angles of depression are 42 and 35 degrees. Find the distance between the two vessels, assuming that they are coming from the same side of the tower.

Answer 1

x is distance between
d is how close the close one is

I assume they are on exactly the same bearing , not just the same side, or the problem is meaningless. People who write math books do not navigate.

tan 42 = 48.8/d

tan 35 = 48.8/(d+x)

so
d = 48.8/tan42
so
d = 54.2
and
54.2 + x = 48.8/tan 35 = 69.7
so
x = 69.7-54.2

Answer 2

thank you for the answer....

Answer 3

15.49

Answer 4

an observed lighthouse 60