Find the length of the shadow on the ground of a pole of height 18 m when angle of elevation $\theta$ of the sun is such that $\tan\theta = \frac{6}{7}$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding rag
Model Answer
Let the length of the shadow be $x$ m. The pole of height 18 m is vertical, so:
$$\tan\theta = \frac{\text{Height of pole}}{\text{Length of shadow}} = \frac{18}{x}$$
Given $\tan\theta = \dfrac{6}{7}$:
$$\frac{6}{7} = \frac{18}{x}$$
$$x = \frac{18 \times 7}{6} = 21 \text{ m}$$
∴ The length of the shadow is 21 m.
Source: Some Applications of Trigonometry, Section 9.1
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Explanation
- Set up a right triangle: pole = opposite side, shadow = adjacent side, so $\tan\theta = \frac{\text{height}}{\text{shadow}}$.
- Substitute the given values and solve for $x$ by cross-multiplication.
- Examiners expect a clear diagram description (or equation setup) and the final answer with units. Two marks: one for correct equation setup, one for correct answer.