A salvage company is using two ships to search for a wrecked plane on the ocean floor. The two ships are 2500 m apart when they make sonar contact with the wreck.

Question

From the first ship, the angle of depression to the plane wreckage is 23°, and from the second ship the angle of depression to the wreck is 31°. Determine the depth of water directly above the wreck, to the nearest metre. Draw labelled diagram

Answer 1

Consider a point P from the first ship at location A, and let AP=k. The other ship is at location B, so PB=2500-k. If P is vertically above the wreck W, then let d=PW=ktan23=(2500-k)tan31,

k(tan23+tan31)=2500tan31,

k=2500tan31/(tan23+tan31)=1465.03m approx.

d=ktan23=621.87m approx.

Depth=622m to nearest metre.