Verified by Ajay Kumar
If \(\tan(\theta)=\frac{12}{5}\) in a right-angled triangle, what is the length of the hypotenuse?
13
15
10
14
Answer: A
Since \(\tan\theta=\frac{\text{Perpendicular}}{\text{Base}}=\frac{12}{5}\), take the perpendicular as 12 and the base as 5. By the Pythagorean theorem, \(H^2=12^2+5^2=144+25=169\). Therefore, \(H=\sqrt{169}=13\). Trick: Recognise the Pythagorean triplet 5, 12, 13.
यदि \(\tan(\theta)=\frac{12}{5}\) एक समकोण त्रिभुज में, कर्ण की लंबाई क्या है?
13
15
10
14
उत्तर: A
चूँकि \(\tan\theta=\frac{\text{लंब}}{\text{आधार}}=\frac{12}{5}\), इसलिए लंब 12 और आधार 5 मानें। पाइथागोरस प्रमेय के अनुसार, \(H^2=12^2+5^2=144+25=169\)। अतः \(H=\sqrt{169}=13\)। ट्रिक: पाइथागोरस त्रिक 5, 12, 13 को पहचानें।
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