Question

You are the navigator of a ship at sea. You receive radio signals from two transmitters A and B, which are 90.0 km apart, one due south of the other. The direction finder shows you that transmitter A is at a heading of 32° south of east from the ship, while transmitter B is due east. Calculate the distance between your ship and transmitter B.

Answer 1

144.03 km

Step-by-step explanation:

The diagram explains better.

From the diagram:

AB = distance between transmitters A and B

AC = distance between transmitter A and the ship

BC = distance between transmitter B and the ship

Using SOHCAHTOA:

tan(A) = BC/AB

AB = 90 km

A = 58°

=>BC = 90 * tan(58)

BC = 144.03 km

The distance between transmitter B and the ship is 144.03 km