Practicing Success
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: |
The value of \(\frac{1}{AB^2}+\frac{1}{BC^2}\)is: |
\(\frac{1}{BD^2}\) \(\frac{1}{AD^2}\) \(\frac{1}{CD^2}\) \(\frac{1}{AC^2}\) |
\(\frac{1}{BD^2}\) |
$tanα=\frac{30}{30\sqrt{3}}=\frac{1}{\sqrt{3}}$ $∴α=30°\, or\, \frac{\pi}{6}$ $tanβ=\frac{30}{10\sqrt{3}}=\sqrt{3}$ $β=\frac{\pi}{3}⇒tan(α+β)=tan(\frac{\pi}{2})$ → ∞ (does not exist) $∠ABC=\frac{\pi}{2}-∞$ $=\frac{\pi}{2}-\frac{\pi}{6}=\frac{\pi}{3}$ $\frac{1}{AB^2}+\frac{1}{BC^2}=\frac{1}{30^2(4)}+\frac{1}{1200}=\frac{1}{3600}+\frac{1}{1200×3}$ $=\frac{4}{3600}=\frac{1}{900}=\frac{1}{BD^2}$ Option 1 is correct. |