Math / Geometry

Question8. Bill placed a mirror on the ground 5 m from the base of a flagpole. He stepped back until he could see the top of the flagpole reflected in the mirror. Bill is 1.5 m tall and saw the reflection when he was 1.25 m from the mirror. How high is the flagpole? lagpole

Studdy Solution

STEP 1

1. The mirror is placed on level ground.
2. The line of sight from Bill's eyes to the top of the flagpole via the mirror forms similar triangles.
3. Bill's height is measured from his eyes to the ground.

STEP 2

1. Identify the similar triangles in the problem.
2. Set up the proportion using the properties of similar triangles.
3. Solve the proportion to find the height of the flagpole.

STEP 3

Identify the similar triangles:
- Triangle 1: Formed by the flagpole, the ground, and the line of sight from the mirror to the top of the flagpole. - Triangle 2: Formed by Bill, the ground, and the line of sight from the mirror to Bill's eyes.

STEP 4

Set up the proportion using the properties of similar triangles:
Let $h$ be the height of the flagpole. The triangles are similar, so:
$\frac{\text{Height of flagpole}}{\text{Distance from mirror to flagpole}} = \frac{\text{Height of Bill's eyes}}{\text{Distance from mirror to Bill}}$
Substitute the given values:
$\frac{h}{5} = \frac{1.5}{1.25}$

STEP 5

Solve the proportion to find $h$ :
Cross-multiply to solve for $h$ :
$h \times 1.25 = 1.5 \times 5$
$h \times 1.25 = 7.5$
Divide both sides by 1.25:
$h = \frac{7.5}{1.25}$
Calculate the division:
$h = 6$
The height of the flagpole is:
$\boxed{6 \text{ m}}$

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