Question

HELP PLEASE! The distances from a ship to two lighthouses on the shore are 4 miles and 7 miles respectively. If the angle between the two lines of sight to the lighthouses is 48 degrees. Find the distance between lighthouses?

Answer 1

Answer:

5.25 miles

Step-by-step explanation:

We are required to determine the distance between Lighthouse A and Lighthouse B in the diagram.

Using Law of Cosines

$c^2=a^2+b^2-2abCosC\\c^2=7^2+4^2-2(7)(4)Cos48^\circ\\c^2=27.5287\\c=\sqrt{27.5287} \\c=5.25\: miles$

The distance between lighthouses is 5.25 miles.