The crows nest of a pirate ship is 22m above the water level. A pirate sitting at the crows nest spots a dolphin at an angle of depression of 15 degrees, in the direction of South 20 degrees East. He also spots a shark at an angle of depression of 23 degrees in the direction of South 45 degrees east. How many meters is the dolphin from the shark?

Relevance
• The crow's nest of a pirate ship is 22 m above the water level.

A pirate sitting at the crow's nest spots a dolphin at an angle of depression of 15°,

in the direction of South 20° East.

He also spots a shark at an angle of depression of 23° in the direction of South 45° East.

How many meters is the dolphin from the shark?

Let d be the distance of the dolphin from the shark.

The dolphin is at a distance of 22 / tan 15° or 82.1051 m

The shark is at a distance of 22 / tan 23° or 51.8288 m

The angle between the dolphin and the shark = 45° - 20° = 25°

d^2 = 82.1051^2 + 51.8288^2 - 2*82.1051*51.8288 cos 25°

d^2 = 1714 m, d = 41.40048... m

The dolphin is at a distance of 41.4 meters from the shark.

• d = distance to dolphin = 22/tan15 = 82.1051 m

s = distance to shark = 22/tan23 = 51.8288 m

Angle between them = 45-20 = 25°

Cosine Rule

x = distance required

x^2 = 82.1051^2 + 51.8288^2 - 2*82.1051*51.8288cos25

x = 41.4 m