Transformations and SymmetrySimilar Triangles

We can use the same technique to measure distances on the ground. Here we want to find the width of a large river. There is a big tree on one side of the river, and I’ve got a stick that is one meter long.

Try drawing another two similar triangles in this diagram.

You can mark the point along the side of the river, that lies directly on the line of sight from the end of the stick to the tree. Then we can measure the distances to the stick, and to the point directly opposite the tree.

Once again, these two triangles are similar because of the AA condition. They both have a right angle, and on pair of opposite angles.

According to the proportionality rule, this means that

COMING SOON – Equation

Therefore the width of the river is 45 meters.