Question:
From the top of a building of height \(h\) meters, the angle of depression of an object on the ground is \(\theta\). What is the distance (in meters) of the object from the foot of the building?
\(h\) मीटर ऊँचाई की एक इमारत के शीर्ष से, जमीन पर एक वस्तु का अवनमन कोण \(\theta\) है। इमारत के पाद से वस्तु की दूरी (मीटर में) क्या है?
Options:
- \(h\cot\theta\)
- \(h\tan\theta\)
- \(h\cos\theta\)
- \(h\sin\theta\)
- \(h\cot\theta\)
- \(h\tan\theta\)
- \(h\cos\theta\)
- \(h\sin\theta\)
Correct Answer: a)
Explanation:
Let \(d\) be the horizontal distance of the object from the foot of the building.
The angle of depression from the top equals the angle of elevation from the object to the top, which is \(\theta\).
In the right triangle:
\[\tan\theta = \frac{h}{d} \implies d = \frac{h}{\tan\theta} = h\cot\theta\]
Hence, the correct option is (a).
माना पाद से क्षैतिज दूरी \(d\) है।
अवनमन कोण = उन्नयन कोण = \(\theta\)।
समकोण त्रिभुज में:
\[\tan\theta = \frac{h}{d} \implies d = \frac{h}{\tan\theta} = h\cot\theta\]
अतः सही विकल्प (a) है।