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Example 2: If B and Q areacute angles such that sin B sin Qthen prove that B ZQ |
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Answer» Answer.∴ AC = k × PR and AB = k × PQFrom right ΔACB, By Pythagoras theorem we haveAB2= AC2+ BC2⇒ (k × PR)2= (k × PQ)2+ BC2⇒ k2× PR2= k2× PQ2+ BC2⇒ BC2= k2× PR2– k2× PQ2 = k2[PR2– PQ2]BC= k root of PR^2-PQ^2From right ΔPRQ, by Pythagoras theorem we havePQ2= PR2+ QR2⇒ QR2= PQ2– PR2 Hence ΔACB ~ ΔPRQ (SSS similarity criterion)∴ ∠B = ∠Q |
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