Hiking a west shore of a river that flows north, you notice a tree on the far shore at a bearing of 30 degrees.

Question

Walk another 100 ft and you're stopped, it's an unclimbable cliff. You consider swimming across river but wonder how wide the river is.

With the tree on the other side at a bearing of 45 degrees, and thinking of what you learned in trig class, you figure out the river is ___ feet wide?

***Consider two right triangles. One of them isosceles, which simplifies things.

Answer 1

about 136.5 feet across the river

let x = distance across the river

tan30 = .577 = x/(100+x)

57.7 + .577x = x

x-.577x = 57.7

.423x = 57.7

x = 57.7/.423

x = about 136.49 feet across the river

construct a right triangle with 30 degrees with opposite side =x = distance across the river, and adjoining side = 100+x.

tangent of 30 degrees = opposite side/adjacent side = x/(100+x)

tan30 = .577 = x/(100+x)

solve for x