Question
Download Solution PDFत्रिभुज ABC में, कोण B = 135° है, AB = 10√2 सेमी और BC = 14 सेमी है। AC की लंबाई क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
त्रिभुज ABC में, कोण B = 135°, AB = 10√2 सेमी और BC = 14 सेमी।
प्रयुक्त सूत्र:
कोज्या नियम का उपयोग करने पर:
\(c^2 = a^2 + b^2 - 2ab \cos(C)\)
गणना:
माना, AB = c = 10√2 सेमी, BC = a = 14 सेमी, और AC = b है।
कोण B = 135°
कोज्या नियम का उपयोग करने पर:
\(b^2 = a^2 + c^2 - 2ac \cos(B)\)
⇒ \(b^2 = 14^2 + (10√2)^2 - 2 \times 14 \times 10√2 \times \cos(135°)\)
⇒ \(b^2 = 196 + 200 - 2 \times 14 \times 10√2 \times -\frac{1}{√2}\)
⇒ \(b^2 = 196 + 200 + 2 \times 14 \times 10\)
⇒ \(b^2 = 676\)
⇒ \(b = 26\) सेमी
∴ सही उत्तर विकल्प (3) है।
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