math
posted by kai on .
Two lookout stations, which are 25 miles apart along the coast on a northsouth line, spot an approaching yacht. One lookout station measures the direction to the yacht at N 33degrees E, and the other station measures the direction of the yacht at S 62degress E. How far is the yacht from each lookout station? How far is the yacht from the coast?

Draw a diagram. If the northern station is at A, and the southern is at B, and the yacht is at C,
angle C is 1806233 = 85°
Using the law of sines,
a/sin62° = b/sin33° = 25/sin85°
a (distance from B) = 22.16
b (distance from A) = 13.67
distance from coast is a sin33° = b sin62° = 12.07