Question

A boat sails on a bearing of 77 degrees for 135 miles and then turns and sails 207 miles on a bearing of 192 degrees. Find the distance of the boat from it’s starting point

Answer 1

193.53 miles

Explanation:

Please see the diagram for understanding of how the angles were derived,

Applying Alternate Angles, ABO =77 degrees

The bearing from B to C is 192=180+12 degrees

Subtracting 12 from 77, we obtain the angle at B as 65 degrees.

We want to determine the boat's distance from its starting point.

In the diagram, this is the line AC.

Applying Law of Cosines:

`b^2=a^2+c^2-2acCosB\\b^2=207^2+135^2-2(207)(135)Cos65^\circ\\b^2=37453.8654\\b=√(37453.8654) \\b=193.53\: miles`

The distance of the boat from its starting point is 193.53 miles (correct to 2 decimal places).