From the top of a mountain a hiker looks at the next mountain top in the distance and notes the compass direction of the peak. He walks some distance at right angles to his initial line of sight and again measures the compass direction to the same peak. Looking at his map he sees that the mountain is 8.72 km away. If the initial compass bearing was 90 degrees, and the new compass bearing is 82 degrees, how far has the hiker walked?