I need help on trigonometry

Question

A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 38°. The distance between the Gladstone and the Norman is 2640 yards. The Norman measures an angle of 57° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager?

Answer 1

This may be solved using the law of sines:

 

A / sin α = B / sin β

 

A = distance between the Norman and Voyager = ?

 

α = angle between the Norman and Voyager = 38 degrees

 

B = distance between the Gladstone and Norman = 2640 yards

 

β = angle between the Gladstone and Norman

 

β = [180 - (38 + 57)] degrees = 85 degrees

 

A / sin α = B / sin β ⇒ A = (sin α / sin β) B = (sin 38 / sin 85) (2640 yards) ≅ 1632 yards