Question

The distance 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 is 45, find the distance between the lighthouses

Answer 1

The distance between the two lighthouse is 5miles

Explanation:

Since the shape of the sketch is a right angled triangle we use SOHCAHTOA to solve. An image showing the step by step working is attached.

Answer 2

5 miles

Explanation:

In the diagram, the distance between the lighthouse is |AB|=c.

Using Cosine Rule,

c²=a²+b²-2abCos C

=7²+4²-2(4)(7)Cos 45°

=49+16-56cos45°

=25.40

c=√25.40=5.04 miles

The distance between the lighthouses is approximately 5 miles.