Two men on either side of a pole of 30 m high observe its top at angles of elevation α and β respectively. The distance between the two men is 40√3 m and the distance between the first man at A and the pole is 30√3m.

Based on the above information, answer the question:

Area of ∆ABD is

450\(\sqrt {3}\)m²

$tanα=\frac{30}{30\sqrt{3}}=\frac{1}{\sqrt{3}}$

$∴α=30° = \frac{\pi}{6}$

$tanβ=\frac{30}{10\sqrt{3}}=\sqrt{3}$

$β=\frac{\pi}{3}$

$tan(α+β)=tan(\frac{\pi}{2})$ → ∞ (does not exist)

Area of ΔABD $=\frac{1}{2}×30\sqrt{3}×30=450\sqrt{3}m^2$

So option 3 is correct.