If a pole is 30 m high, casts a shadow \(10\sqrt{3}\) m long on the ground, then the angle of elevation of the sun is:
60°
The pole is vertical and its shadow is along the ground, so they form a right-angled triangle with the angle of elevation \(\theta\) at the tip of the shadow.
Here the pole (height) is the side opposite to \(\theta\) and the shadow is the side adjacent to \(\theta\), so \(\tan\theta = \dfrac{\text{height}}{\text{shadow}}\).
Substituting the values: \(\tan\theta = \dfrac{30}{10\sqrt{3}} = \dfrac{3}{\sqrt{3}} = \sqrt{3}\).
Since \(\tan 60^\circ = \sqrt{3}\), we get \(\theta = 60^\circ\).
Hence, the angle of elevation of the sun is 60°.
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