Discussion
A tower is 100√3 metres high. Find the angle of elevation of its top from a point 100 metres away from its foot.
Answer: D
The tower is opposite the angle of elevation and the 100 m is the adjacent side, so the tangent gives the angle directly.
\[ \tan\theta = \frac{100\sqrt{3}}{100} = \sqrt{3} \]
\[ \theta = 60^{\circ} \]
The three standard tangents are worth knowing by sight: \( \tan 30^{\circ} = \tfrac{1}{\sqrt{3}} \), \( \tan 45^{\circ} = 1 \) and \( \tan 60^{\circ} = \sqrt{3} \). Since the tower is taller than the distance, the angle must exceed \( 45^{\circ} \).
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