Question
Download Solution PDFदिलेल्या आकृतीमध्ये जर AD ⊥ BC, AC = 26 एकक, CD = 10 एकक, BC = 42 एकक, ∠DAC = x आणि ∠B = y तर
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
AD ⊥ BC ; ∠D = 90°
AC = 26 एकक; CD = 10 एकक; BC = 42 एकक
∠DAC = x आणि ∠B = y
वापरलेले सूत्र:
पायथागोरस प्रमेय:
H2 = P2 + B2
Cos θ = B/H ; tan θ = P/B
जिथे, H = कर्ण ; P = लंब; B = पाया
गणना:
△DAC मध्ये
⇒ AC2 = AD2 + CD2
⇒ 262 = AD2 + 102
⇒ 676 = AD2 + 100
⇒ AD = √(676 - 100) = √576 = 24 एकक
△ADB मध्ये
BD = (BC - CD) = (42 - 10) = 32 एकक
⇒ AB2 = AD2 + BD2
⇒ AB2 = 242 + 322
⇒ AB2 = 576 + 1024
⇒ AB = √1600 = 40 एकक
प्रश्नावरून:
⇒ 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 एकक
∴ 25/4 एकक हे योग्य उत्तर आहे.
Last updated on Jul 21, 2025
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