Question

island alea is 240 miles from the island bert. a shop captain travels 180 miles from island ale, and then realizes he is off course and 100 miles from island bert. at what angle must the captain turn the ship in order to head straight to bert.

Answer 1

Use the cosine rule:
240²=180²+100²-2×180×100cosθ where θ is the angle between the original course and the altered course.
57600-32400-10000=-36000cosθ; 15200=-36000cosθ, cosθ=-15200/36000=19/45, θ=114.97°. This is the angle the captain must turn the ship.