As observed from the top of a 80 m tall light house, the angles of depression of two ships on the same side of the light house in horizontal line with its base are 30⁰ and 40⁰ respectively. Find the distance between the two ships. Give your answer correct to the nearest metre.

Solution:

Consider AB as the light house and C and D as the two ships.

In triangle ADB

tan 30⁰ = AB/BD

Substituting the values

1/√3 = 80/BD

So we get

BD = 80√3…… (1)

In triangle ACB

tan 40⁰ = AB/BC

Substituting the values

0.84 = 80/BC

So we get

BC = 80/0.84 = 95.25

Using equation (1)

BD = 80 √3 = 80 × 1.73 = 138.4

Here we get

DC = BD – BC

DC = 138.4 – 95.25 = 43.15

Therefore, the distance between the two ships is 43.15 m.