The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places:
Situation – I: The angle of elevation of the top of Statue from Place A which is $80\sqrt{3}$ m away from the base of the Statue is found to be 60°.
Situation – II: The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be 30° and entire height of the Statue including the base is found to be 240 m.
Based on given information, answer the following questions.
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding stimulus
Model Answer
(i) Diagram – Situation I:
```
|
| h
|
|___________
| Base | A (observer on ground)
|___________|←——— 80√3 m ———→
∠60°
```
A right triangle with observer A on ground, horizontal distance = 80√3 m, angle of elevation = 60°.
---
(ii) Diagram – Situation II:
```
|
|
|
_____|
| |←——— d ———→ B (40 m above ground)
|240m| ∠30°
|___|
```
Observer B is 40 m above ground; angle of elevation to top = 30°; total height = 240 m.
---
(iii) Calculation using Situation – I:
Let total height of statue (including base) = H m.
$$\tan 60° = \frac{H}{80\sqrt{3}}$$
$$\sqrt{3} = \frac{H}{80\sqrt{3}}$$
$$H = 80\sqrt{3} \times \sqrt{3} = 80 \times 3 = 240 \text{ m}$$
Height including base = 240 m
Height excluding base = 240 – 58 = 182 m
Source: Some Applications of Trigonometry, NCERT Class 10 Maths
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Explanation
- For (i) and (ii), even a rough labelled sketch earns the mark — label the angle, distance, and height clearly.
- For (iii), examiners award 1 mark for correct use of tan 60° and setting up the equation, and 1 mark for the final answers (240 m and 182 m). Always subtract the given base height (58 m) to find the statue height alone.
- Key formula: $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$