Kurt wants to sail his boat from a marina to an islnd 15 miles east of the marina. Along the course, there are several small islands they must avoid. He sails first on a heading of 70 degrees and then on a heading of 120 degrees. What is the total distance he travels before reaching the island?

Answer 1

70 is 20 north of east
120 is 30 south of east
draw that triangle with your two courses and the x (east) axis
your triangle has angles 20, 30 with leg 15 between
the angle at the top, opposite the 15 miles is therefore
180 - 50 = 130
then law of sines
sin30/leg1 = sin130/15
so leg1 = 9.8

sin20/leg2 = sin130/15
so leg2 = 6.7
9.8+6.7 = 16.5 miles