Math Explanation and Solution

Question

In a flooded area, Cora is stranded at a point 70° west of north with respect to the central base of rescue operations. The nearest rescue boat is docked 40° east of north with respect to the central base. If the boat is 100 m away from the central base and Cora’s location is 75° west of north with respect to the boat, then how far away is the boat from where Cora is?

Answer 1

Make a sketch with base B at the origin, Cora's boat C at some distance in 2nd quadrant at angle 20° above negative x axis, and rescue boat R in 1st quadrant 50° above positive x axis. Length BR is 100 m. Angle B is 180 - (20+50) = 110°. Angle R is trickier: imagine a ray parallel to x axis extending left from point R; this makes a 50° angle with segment BR. The angle from R to C is 15° above this line, so angle R is 50 + 15 = 65°. Therefore angle C is a mere 5°.

Law of Sines gives us CR / sin B = 100 / sin C, CR = 100 (0.9397) / (0.08716) = 1,078 m.