Question

A plane leaves Seattle, flies 76.0 mi at 22.0 ∘ north of east, and then changes direction to 51.0 ∘ south of east. After flying at 123 mi in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew.
In what direction should the crew fly to go directly to the field? Use components to solve this problem

How far should the crew fly to go directly to the field? Use components to solve this problem.

Answer 1

This can be solve by using a triangle, because the path of the plane formed a triangle. first solve the angle form by the second direction
angle = 180 - 51 - 22 = 107 degrees
then using the cosine law
c^2 = a^2 + b^2 - 2ab cos C
c^2 = 76^2 + 123^2 - 2 ( 76) ( 123) cos ( 107)
c = 162.4 mi the crew fly to go directly to the field