Question

A ship at sea, the Admiral, spots two other ships, the Barstow and the Cauldrew and measures the angle between them at be 45°. They radio the Barstow and by comparing known landmarks, the distance between the the Admiral and the Barstow is found to be 323 meters. The Barstow reports an angle of 59° between the Admiral and the Cauldrew. To the nearest meter, what is the distance between the Barstow and the Cauldrew?

Answer 1

235 Meters

Explanation:

The pictorial representation is produced and attached.

In Triangle ABC, we want to determine the distance between the Barstow and the Cauldrew(i.e. B and C).

`\angle A+\angle B+\angle C=180^\circ\\45+59+\angle C=180^\circ\\\angle C=180^\circ-45^\circ-59^\circ\\\angle C=76^\circ`

Using Law of Sines

`(a)/(Sin A)= (c)/(Sin C)\\\\(a)/(Sin 45)= (323)/(Sin 76)\\\\a*Sin 76=323*sin45\\\\a=(323*sin45)/ Sin 76\\a\approx 235\:meters`

The distance between the Barstow and the Cauldrew is 235 meters to the nearest meter.