Question

A captain knows that his ship is due south of a lighthouse. His destination is 20 km due west of the lighthouse, on a course setting of 40° west of the lighthouse. How far south of the lighthouse is the ship?

Answer 1

The ship is approximately 12.86 km south of the lighthouse.

To solve this problem

Solution:

• The lighthouse is straight south of the ship.
• 20 kilometers straight west of the lighthouse is the destination.
• The course is located 40° to the west of the lighthouse.

Trigonometric relationship:

We can use the Sine rule to solve for the distance S:

S / sin(40°) = 20 km / sin(90°)

Solving for S:

S = 20 km * sin(40°) / sin(90°)

S ≈ 12.86 km

So, the ship is approximately 12.86 km south of the lighthouse.