Question

Lighthouse B is 9 miles west of lighthouse A. A boat leaves A and sails 4 miles. At this​ time, it is sighted from B. If the bearing of the boat from B is N​E65, how far from B is the​ boat?

Answer 1

The distance of the boat from B is approximately 9.4 miles

Explanation:

The location of light house B from A = 9 miles west

The distance of the boat from A = 4 miles

The bearing of the boat from A = NE65

We have;

4/(sin25) = 9/sin(B)

sin B = 9*sin(25)/4

B ≈ 71.969

a² = 4² + 9² - 2 × 4 × 9 × cos(180 - 25 - 71.969) ≈ 88.264

The distance of the boat from B, a ≈ √88.264 ≈ 9.4