Question

rachel is trying to measure the height of a nearby flagpole using a mirror as shown in the diagram. the mirror is 4 meters away from the flagpole and 2.4 meters away from rachel. the height to her eyes is 1.8 meters, from which she can clearly see the top of the flagpole. how tall is the flagpole? the height of the flagpole is \boxed{} meters.

Explanation:

Step1: Identify similar triangles

The two triangles (flagpole - mirror and Rachel - mirror) are similar, so their corresponding sides are proportional. Let \( x \) be the height of the flagpole. The proportion is \(\frac{x}{4}=\frac{1.8}{2.4}\).

Step2: Solve for \( x \)

Cross - multiply: \( 2.4x = 4\times1.8 \).
Calculate the right - hand side: \( 4\times1.8 = 7.2 \).
Then, \( x=\frac{7.2}{2.4} \).
Simplify the fraction: \( x = 3 \).

Answer:

3