Question

A ship is anchored off a long straight shoreline that runs north and south. From two observation points 17 miles apart on shore, the bearings of the ship are N 32° E and S 53° E. What is the shortest distance from the ship to the shore? (Round your answer to the nearest tenth.)

Answer 1

d - the shortest distance from the ship to the shore.
d / ( 17 - x ) = tan 32° = 0.62487
d / x = tan 53° = 1.32704
d = 0.62487 ( 17 - x )
d = 1.32704 x
0.62487 ( 17 - x ) = 1.32704 x
10.62279 - 0.62487 x = 1.32704 x
x = 10.62279 : 1.95191
x = 5.44226 miles
d = 5.44226 · 1.32704
Answer:
d = 7.222  miles