Question
Download Solution PDFयदि कोई ΔABC , ∠C = 75°, ∠B = 45° और a = √3 हो, तो b का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
त्रिभुज ABC में, ज्या नियम के अनुसार
\(\rm \frac{a}{\text{sin A}}=\frac{b}{\text{sin B}}=\frac{c}{\text{sin C}}\)
जहाँ, a, b, c भुजाएँ हैं और A, B, C त्रिभुज के कोण हैं।
त्रिभुज में कोणों का योग 180° होता है
गणना:
दिया गया है: ∠C = 75°, ∠B = 45° और a = √3
∠A + ∠B + ∠C = 180°
⇒ ∠A = 180° - 75° - 45°
⇒ ∠A = 60°
ज्या नियम
\(\frac{a}{\text{sinA}}=\frac{b}{\text{sinB}}\)
⇒ \(\rm \frac {√3}{sin\ 60^0}\ = \ \frac {b}{sin\ 45^0}\)
⇒ \(\rm \frac {√3}{\frac {√3}{2}}\ = \ \frac {b}{\frac {1}{√2}}\)
⇒ \(\rm b\ = \frac {2}{√2}\)
⇒ b = √2
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