Question
Download Solution PDFदिए गए चित्र में यदि AD ⊥ BC, AC = 26 इकाई, CD = 10 इकाई, BC = 42 इकाई, ∠DAC = x और ∠B = y है, तो \(\rm \frac{6}{\cos x}-\frac{5}{\cos y}+8\tan y\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
AD ⊥ BC; ∠D = 90°
AC = 26 इकाई; CD = 10 इकाई; BC = 42 इकाई
∠DAC = x और ∠B = y
प्रयुक्त सूत्र:
पाइथागोरस प्रमेय:
H2 = P2 + B2
Cos θ = B/H; tan θ = P/B
जहाँ, H = कर्ण; P = लंब; B = आधार
गणना:
△DAC में
⇒ AC2 = AD2 + CD2
⇒ 262 = AD2 + 102
⇒ 676 = AD2 + 100
⇒ AD = √(676 - 100) = √576 = 24 इकाई
△ADB में
BD = (BC - CD) = (42 - 10) = 32 इकाई
⇒ AB2 = AD2 + BD2
⇒ AB2 = 242 + 322
⇒ AB2 = 576 + 1024
⇒ AB = √1600 = 40 इकाई
प्रश्न से:
\(\rm \frac{6}{\cos x}-\frac{5}{\cos y}+8\tan y\)
⇒ 6/(AD/AC) - 5/(BD/AB) + 8 × (AD/BD)
⇒ 6/(24/26) - 5/(32/40) + 8 × (24/32)
⇒ (6 × 26/24) - (5 × 40/32) + 8 × (24/32)
⇒ 6.5 - 6.25 + 6
⇒ 6.25 = 25/4 इकाई
∴ सही उत्तर 25/4 इकाई है।
Last updated on Jul 22, 2025
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