Question

For a project in her Geometry class, Shandra uses a mirror on the ground to measure the height of her school’s flagpole. She walks a distance of 13.35 meters from the flagpole, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.55 meters to the other side of the mirror, until she can see the top of the flagpole clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.25 meters. How tall is the flagpole? Round your answer to the nearest hundredth of a meter.

Answer 1

To determine the height of the flagpole, we can use similar triangles. Using the properties of similar triangles, we can set up a proportion and solve for the height of the flagpole.

The height of the flagpole is approximately 3.20 meters.

Step-by-step explanation:

To determine the height of the flagpole, we can use similar triangles. Let's say the height of the flagpole is x meters.

From the given information, we can create a right triangle with one leg of length 13.35 meters and the other leg of length 1.55 meters. The height of the flagpole would be the longer leg of the triangle.

Using the properties of similar triangles, we can set up the following proportion:

(1.55 - 1.25) / 1.25 = x / 13.35

Simplifying the proportion, we get:

0.3 / 1.25 = x / 13.35

Now, we can cross multiply and solve for x:

x = (0.3 / 1.25) * 13.35 = 3.204 meters

Therefore, the height of the flagpole is approximately 3.20 meters.