Question

Jamie needs to determine the distance across a river. She selects a rock, R, on the opposite river bank. She finds a tree, T, on her side of the river such that is perpendicular to the river. Next, Jamie walks 50 yards down the river from the tree, T, to a spot, C. Using a compass that she made from two sticks, she measures . She then walks from C in a direction that makes the same angle as with the river bank on her side of the river. She keeps walking in that direction until she sees the tree and the rock in a straight line from her position. She marks this point B and then paces from B to T to measure the distance from point B to the tree. If BT turns out to be 75 yards, what is RT, the distance across the river?

Answer 1

RT = BT = 75

This is because she used the same angle from point C to mark point B, thus creating a symmetric right triangle.

Triangle BCT = Triangle RCT