Expert: Richard J. Raridon - 3/28/2004

Question
1. IN triangle HJK m angle k = 81 degrees, k = 21, and j = 20 find angle J.

2. an observer in a lighthouse on the shore sees a ship in distress. The ship is 15 miles away at an angle of 20 degrees with the shoreline. A coast guard station is on the shoreline 30 miles away from the ligthhouse.
a. how far will a coast guard rescue ship have to travel from the station to reach the ship?
b. the path of the rescue vesssel should be at what angle to the shoreline(use your ans.. to part a.)  

Answer
1. 21/sin(81) = 20/sin(x), x = 70.2 degrees
2. I assume the coast guard station is on the same side of the lighthouse as the ship in distress. First you can calculate the perpendicular distance from the shore to the ship.  d = 15sin(20) = 5.13 miles.  The distance from this perpendicular point is 14.1 miles from the lighthouse and, therefore, 15.9 miles from the coast guard station.  
b. the angle of the path is A, where tanA = 5.13/15.9, so
A = 17.88 degrees
a. the distance to the ship is R, where sin(17.88) = 5.13/R
so R = 16.7 miles