Question

A fire is spotted 29 degrees west of South. The fire is 58 km from the look out station. A fire fighting base is 62 km due west of the first station. How far is the fire from the fighting base?

Answer 1

If the lookout is at the origin, the base is at `(-62,0)` and the fire is at `(-58 sin 29^circ, -58 cos 29^circ)` so the distance is

`d=\sqrt{(62-58 \ sin 29^circ)^2+58 \ cos^2 29^circ} approx 34.5` km