HELP WITH PHYSICS QUESTION!!?!?!?

Question

A lost hiker walks 2 km due south, then 3 km in another direction. He then looks at his GPS, and finds that he is 4 km from his starting point. Where is he located relative to the starting position?

Answer 1

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Unless that hiker was near enough to one of the poles that the fact that latitude lines aren't straight and meridians aren't parallel matters, then this is a plane trigonometry problem.

Let A be the starting point, B be the point 2 km south of A, and C be the end point 3km from B and 4 km from A. Sketch the triangle ABC and label the sides a,b,c opposite angles A, B, C respectively. Standard setup, right? a=3, b=4, c=2 are given in the problem.

The law of cosines for angle A is:

a^2 = b^2 + c^2 - 2bc cos A

...can be solved for angle B as:

A = cos⁻¹ [(b^2 + c^2 - a^2) / (2bc)] ~~ 46.57 degrees

Point C is 4 km from A, bearing 46.56 degrees either east or west of due south.

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