You are hiking along the west shore of a river thats flowing

You are hiking along the west shore of a river that\'s flowing due north. You notice a tree on the far shore at a bearing of 30 degrees. You walk on for another 100 feet and you are stopped by an unclimbable cliff. You contemplate swimming across the river and wonder how wide it is. The tree on the other side now appears at a bearing of 45 degrees. Remembering your trig class, you figure out that the river is feet wide.

Solution

Considering two right triangles

Bearings : tan(30) = sqrt(3)/3
                   tan(45) = 1

Let the width of river be w:

sqrt(3)/3 = w/(100 + x)
1 = w/x
w = x

sqrt(3)/3 = w(100 + w)
57.7 + .577w = w
.423w = 57.7
w = 57.7/.423 = 136.41 ft