# Modeling Similar/Congruent Triangles

### Example 1. You spot a drone flying at a certain height 54 m horizontally from where you stand, as shown in the figure below. How high up is the drone? The triangle formed by you and the point on the ground is similar to the triangle formed by the height of the drone and the point on the ground. We have:

1.8/6 = h/60

--> h = 1.8 * 60 / 6

--> h = 18 m

### Example 2. A diver is 5.5 ft tall. He is standing 10 ft from the edge of a 35 ft tall cliff. Find the horizontal distance between the diver and the boat. The triangle formed by the diver and the edge of the cliff is similar to the triangle formed by the cliff and the boat. We let the horizontal distance between the cliff and the boat be x. We have:

5.5/10 = 35/x

--> x = 63.64 ft

Horizontal distance between you and the boat is 10 + 63.64 = 73.64 ft.

### Example 3. A statue stands x meters tall. Find x. The triangle formed by the statue and the point on the ground is similar to the triangle formed by the person and the point on the ground. We have:

x/4 = 1.8/2.4

--> x = 1.8 / 2.4 * 4

--> x = 3 m

### Example 4. A few hikers come to a river and need to figure out how wide it is. On their map, they trace out two triangles as shown. What is length GH? We realize that the two triangles drawn are congruent by ASA. We can then use the theorem CPCTC, which means the corresponding side for GH is length GH. We have:

JK = GH = 5 m