Answer:
Distance between the lighthouses is 26.78 miles.
Explanation:
Distance between the ship A and lighthouse B = 18 miles
Distance between ship B and lighthouse C = 30 miles
Angle formed at the ship to both the lighthouses = 62°
By applying cosine rule in the given triangle,
(BC)² = (AB)² + (AC)² - 2(AB)(AC)cos(∠A)
(BC)² = (30)² + (18)² - 2(30)(18)cos(62°)
(BC)² = 900 + 324 - 507.03
= 716.97
BC = √716.97 = 26.78 miles
Therefore, distance between the lighthouses is 26.78 miles.