Section 6.1 Looking for the set up only. [ATTACH=full]1611[/ATTACH]
Since the boat is traveling at a rate of 10 miles per hour (60 minutes), that same boat travels 2.5 miles in 15 minutes. Draw a diagram. [On the diagram shown, all angles are in degrees.] This diagram should show two triangles -- one with a 72° angle to the lighthouse, and another with a 66° angle to the lighthouse. Find the complementary angles of 18° and 24°. The angle immediately under the boat's present location measures 66°+90°=156°. For the angle with the smallest measure in the diagram, I have used the fact that 6°=24°−18°, but you may also subtract the sum of 156° and 18° from 180°. This gives us an oblique triangle whose angles measure 156°,18°,and 6° and one of whose sides measures 2.5 miles. You may now use the Law of Sines to find the direct distance to the lighthouse. sin6°/2.5=sin18°/d This gives a direct distance of approximately 7.4 miles. If you want the perpendicular distance to the shore, you may now use basic trigonometry. If y is the perpendicular distance, then y/7.4=sin23° y=7.4/sin23° This is approximately 2.9 miles.
