Answer to Question #252314 in Trigonometry for Yonti

Question

An observer on a lighthouse in an island 150 feet height above the sea level saw two vessels moving directly towards the lighthouse. He observed that the angle of depression of the vessels are 39 degrees and 25 degrees. Find the distance between the two vessels, assuming that they are coming from the same side of the tower.

Answer 1

distance of first vessel from lighthouse:

$L_1=150/tan39\degree=185.23$ ft

distance of second vessel from lighthouse:

$L_2=150/tan25\degree=321.68$ ft

the distance between the two vessels:

$L=L_2-L_1=321.68-185.23=136.45$ ft