Question

Calculating Distances at Sea The navigator of a ship at sea spots two lighthouses that she knows to be 3 miles apart along a straight seashore. She determines that the angles formed between two line-of-sight observations of the lighthouses and the line from the ship directly to shore are 15° and 35°. See the illustration.

(a) How far is the ship from lighthouse P?

(b) How far is the ship from lighthouse Q?

(c) How far is the ship from shore?

Short answer

(a) The distance from the ship to the lighthouse P is 3.21 miles.

(b) The distance from the ship to the lighthouse Q is 3.78 miles.

(c) The distance from the ship to the shore is 3.1 miles.

Step-by-step solution

Step 1. Given Information

A ship sees two lighthouses 3 miles apart on the shore.

The angle between the line that connects the ship and the lighthouse P and the line from the ship directly to the shore is ${15}^{\circ }.$

The angle between the line that connects the ship and the lighthouse Q and the line

from the ship directly to the shore is ${35}^{\circ }.$