Question

Two friends, Keith and Jamal, who have gone hiking in the woods have become separated. Keith has walked for an unknown distance before realizing that his friend is not near. Keith then walks 0.5 km due north to look for Jamal, but sends up a flare signal when he cannot find him, then waits. Meanwhile, Jamal has walked 1.3 km at 35° south of west, but after seeing the flare he walks 1.6 km 15° east of north to meet Keith. How far and in what direction did Keith wander when he and Jamal first became separated?

The answer given is 0.7km at 25° north of west, but I'm not sure how to get this answer.

Answer 1

Let us first draw the path of Jamal.

Now, let's trace back the path of Keith. Keith has walked 0.5 km due north. So, the path of Keith would be

We have to find the distance OC and angle theta.

To find this let us first find the coordinates of points A, B, and C.

The coordinates of point A are

The coordinates of point B are

And the coordinates of point C are

So, the distance OC is

And the angle is