Posted by tareena on .
a fire is sighted from two ranger stations that are 6000 meters apart. The angles of observation to the fire measure 52 degrees from one station and 41 degrees from the other station. Find the distance along the line of sight to the fire from the closer of the two stations.

math 
drwls,
Draw yourself a triangle with points at Station 1 (A), Station 2 (B), and the fire (C). A is closest to the fire. The distance from A to B is c = 6000 m. The inside angles are A = 18052 = 128, B = 41 and C = 18041128 = 11 degrees. Use the law of sines to determine b.
sin 11/6000 = sin 41/b 
math 
Reiny,
This is a good question showing how two different but valid interpretations can be had.
Without looking first at drwls solution I made a sketch and placed the angles of 52º and 41º inside the triangle
and my sine law equation would have been
b/sin41 = 6000/sin87 resulting in a different answer.
A diagram in your text of course would eliminate one of the interpretations, and is the reason why a text often shows a picture for you.
A fairminded teacher should accept both solutions as correct.