Question
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?
Answers
Damon
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
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