Discussion
When the Sun's altitude is 30°, the shadow of a tower is 15 meters long. What will be the length of the shadow when the Sun's altitude is 60° ?
Answer: B
The shadow will be 5 meter long.
The tower's height is the shadow length times the tangent of the Sun's altitude:
\[ \begin{aligned} h &= 15 \tan 30^{\circ} = \frac{15}{\sqrt{3}} = 5\sqrt{3} \\ s &= \frac{h}{\tan 60^{\circ}} = \frac{5\sqrt{3}}{\sqrt{3}} = 5 \end{aligned} \]
Since \(\tan 60^{\circ} = 3 \tan 30^{\circ}\), the shadow at 60° is one-third of the shadow at 30°. 4, 3 and 6 metres do not give that ratio.
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