Use similar triangles to find unknown lengths in application problems

To determine the height of a flagpole, a woman walks to a point 20 feet from its base, places a mirror on the ground, then steps back 2 feet farther — where she can see the top of the pole reflected in the mirror. Her eye level is 5 feet from the ground. Find the height \(h\) of the flagpole.

The two right triangles formed are similar. Set up and solve the proportion to find \(h\).

In the figure below, \(\triangle ABC \sim \triangle EDC\). Find \(h\).

A person who is 6 feet tall casts a shadow 4 feet long. At the same time, a nearby tree casts a shadow 20 feet long. The triangles formed are similar. Find the height \(h\) of the tree.

A 3-foot stake held vertically in the ground casts a shadow 2 feet long. At the same time, a building casts a shadow 30 feet long. The triangles are similar. What is the height \(h\) of the building?

A surveying crew needs to find the width of the river shown in the illustration below. Because of a dangerous current, they decide to stay on the west side of the river and use geometry to find its width. Their approach is to create two similar right triangles on dry land.Then they write and solve a proportion to find .

What is the width of the river?

Answer = 1($) ft