# HELP WITH PHYSICS 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?

### 1 Answer

- husoskiLv 73 years agoFavorite Answer
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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