Discussion

At a certain moment the length of the shadow of a pole is \( \sqrt{3} \) times the height of the pole. The angle of elevation of the sun is:

Answer: A

The angle of elevation \( \theta \) satisfies

\[ \tan\theta = \frac{\text{height of pole}}{\text{length of shadow}} \]

With the shadow \( \sqrt{3} \) times the height \( h \):

\[ \tan\theta = \frac{h}{\sqrt{3}\,h} = \frac{1}{\sqrt{3}} \quad\Longrightarrow\quad \theta = 30^{\circ} \]

The pole's height cancels, so no measurement is needed. A shadow longer than the object always means the sun is below \( 45^{\circ} \).

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