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Chapter 8: Q. 50 (page 529)

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掳 and 35掳. 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

Expert verified

(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

01

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鈭�.

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鈭�.

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