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
Answer & explanation
Correct answer: option 3
$tanα=\frac{30}{30\sqrt{3}}=\frac{1}{\sqrt{3}}$
$∴α=30° = \frac{\pi}{6}$
$tanβ=\frac{30}{10\sqrt{3}}=\sqrt{3}$
$β=\frac{\pi}{3}$
$tan(α+β)=tan(\frac{\pi}{2})$ → ∞ (does not exist)
Area of ΔABD $=\frac{1}{2}×30\sqrt{3}×30=450\sqrt{3}m^2$
So option 3 is correct.