Solve the problem.
-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?
A) 81 m
B) 235 m
C) 49 m
D) 266 m

Question

Quizplus · Accepted Answer

The Law of Sines can be used to solve this problem. The ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle. In this case, we have:$$\frac{d_1}{\sin 45°} = \frac{d_2}{\sin 59°}$$where $d_1$ is the distance between the Admiral and the Barstow, $d_2$ is the distance between the Barstow and the Cauldrew, and the angles are as shown in the diagram.We know that $d_1 = 323$ meters, so we can solve for $d_2$:$$\frac{323}{\sin 45°} = \frac{d_2}{\sin 59°}$$$$d_2 = \frac{323 \sin 59°}{\sin 45°} \approx 235 	ext{ meters}$$Therefore, the distance between the Barstow and the Cauldrew is approximately 235 meters.

Solve the Problem. -A Ship at Sea, the Admiral, Spots Two Other Ships