त्रिकोण PQR मध्ये, PQR हा काटकोन आहे. PRQ  हा कोन  60° चा आहे आणि बाजू PR ची लांबी 20 सेमी आहे. तर बाजू QR ची लांबी किती आहे?

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ISRO VSSC Technician-B Fitter 10 Dec 2017 Official Paper
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  1. 10
  2. 20
  3. 40
  4. 15

Answer (Detailed Solution Below)

Option 1 : 10
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दिलेले:

त्रिकोण PQR  हा काटकोन त्रिकोण आहे.

∠PQR = 90° 

∠PRQ = 60°

PR = 20 सेमी 

वापरलेली संकल्पना:

त्रिकोणाच्या सर्व आंतरकोनांच्या मापांची बेरीज 180° असते. 

sin θ = P/H

गणना:

सर्व आंतरकोनांच्या मापांची बेरीज  = 180° 

⇒ ∠PQR + ∠PRQ + ∠RPQ = 180° 

⇒ 90° + 60° + ∠RPQ = 180°

⇒ ∠RPQ = 180° – 150° = 30° 

आता, sin 30° = P/H

⇒ sin 30° = QR/PR

⇒ 1/2 = QR/20

⇒ QR = 10

∴ बाजू QR ची लांबी 10 सेमी आहे.

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