A 25 cm stick casts a 20 cm shadow. A nearby pole casts a 5 m shadow. How tall is the pole?

Question

ScanSolve AI Tutor · Accepted Answer

This problem involves similar triangles, as the angle of elevation of the sun is the same for both the stick and the pole.

Identify the given values and ensure consistent units.
Height of the stick ( $H_s$ ) = $25 \text{ cm}$
Length of the stick's shadow ( $L_s$ ) = $20 \text{ cm}$
Length of the pole's shadow ( $L_p$ ) = $5 \text{ m}$

Convert the pole's shadow length to centimeters for consistency:
$L_p = 5 \text{ m} \times 100 \frac{\text{cm}}{\text{m}} = 500 \text{ cm}$
Set up the proportion using similar triangles.
The ratio of the height of an object to the length of its shadow is constant.
$\frac{H_s}{L_s} = \frac{H_p}{L_p}$
where $H_p$ is the height of the pole.
Substitute the known values into the proportion.
$\frac{25 \text{ cm}}{20 \text{ cm}} = \frac{H_p}{500 \text{ cm}}$
Solve for $H_p$ .
$H_p = \frac{25}{20} \times 500 \text{ cm}$ $H_p = \frac{5}{4} \times 500 \text{ cm}$ $H_p = 5 \times \frac{500}{4} \text{ cm}$ $H_p = 5 \times 125 \text{ cm}$ $H_p = 625 \text{ cm}$
Convert the height of the pole back to meters if desired, or keep in centimeters.
$H_p = 625 \text{ cm} = \frac{625}{100} \text{ m} = 6.25 \text{ m}$
The height of the pole is $\boxed{625 \text{ cm}}$ or $\boxed{6.25 \text{ m}}$ .

Answer