Question : If the length of the shadow of a vertical pole is $\sqrt{3}$ times the height of the pole, the angle of elevation of the sun is:
Option 1: $60°$
Option 2: $45°$
Option 3: $30°$
Option 4: $90°$
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Correct Answer: $30°$
Solution : Given: The length of the shadow of a vertical pole is $\sqrt{3}$ times the height of the pole. Let $h$ be the height of the pole and $\theta$ be the sun's elevation angle. Then from the figure, we can get AB = $h$ unit and BC = $\sqrt{3}h$ unit. Now applying the formula $\tan\theta=\frac{\text{Perpendicular}}{\text{Base}}$ we get, $\tan\theta=\frac{h}{\sqrt{3}h} = \frac{1}{\sqrt{3}} = \tan30°$. ⇒ $\theta=30°$ Hence, the correct answer is 30°.
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Question : If the angle of elevation of the sun decreases from $45^\circ$ to $30^\circ$, then the length of the shadow of a pillar increases by 60 m. The height of the pillar is:
Question : Find the angular elevation of the Sun when the shadow of a 15 metres long pole is $\frac{15}{\sqrt{3}}$ metres.
Question : The length of the shadow of a vertical tower on level ground increases by 10 m when the altitude of the sun changes from 45° to 30°. The height of the tower is:
Question : The shadow of a tower when the angle of elevation of the sun is 45°, is found to be 10 metres longer than when it was 60°. The height of the tower is:
Question : If the elevation of the Sun changes from 30° to 60°, then the difference between the lengths of shadows of a pole 15 metres high, is:
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