Question

example 8
a pole and a stick stand vertically on a level ground. the stick is 25 cm long and casts a shadow of length 20 cm. if the pole casts a shadow of length 5 m, what is the height of the pole?
solution
in fig 24.25, dc represents the pole of height h m.
the angle of elevation of the sun is the same for both the stick and the pole.
in right - angled triangle abe, tanθ=\frac{be}{ab}=\frac{25}{20}=1.25......(1)
in right - angled triangle acd

Explanation:

Step1: Set up proportion

Since the two - triangles formed by the stick and its shadow and the pole and its shadow are similar (because the angle of elevation of the sun is the same for both), the ratios of height to shadow length are equal. Let the height of the pole be $h$. We have the proportion $\frac{\text{height of stick}}{\text{length of stick's shadow}}=\frac{\text{height of pole}}{\text{length of pole's shadow}}$.

Step2: Convert units

The length of the stick is $25$ cm, the length of the stick's shadow is $20$ cm, and the length of the pole's shadow is $5$ m. Convert $5$ m to cm: $5$ m $ = 500$ cm.

Step3: Substitute values into proportion

Substituting the values into the proportion $\frac{25}{20}=\frac{h}{500}$.

Step4: Solve for $h$

Cross - multiply: $20h=25\times500$. Then $20h = 12500$. Divide both sides by $20$: $h=\frac{12500}{20}=625$ cm. Convert back to meters: $h = 6.25$ m.

Answer:

The height of the pole is $6.25$ m.