Question
Download Solution PDFएक ΔABC में यदि a = 18, b = 24 और c = 30 है तो sin (A/2) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि a, b और c, ΔABC की भुजाएं इस प्रकार हैं जिससे a + b + c = 2S है, तो \(\sin \frac{A}{2} = \sqrt {\frac{{\left( {S - b} \right)\left( {S - C} \right)}}{{bc}}} \)
गणना:
दिया गया है: ΔABC के लिए हमारे पास a = 18, b = 24 और c = 30 हैं।
यहाँ, हमें sin (A/2) का मान ज्ञात करना है।
चूँकि हम जानते हैं कि, यदि a, b और c, ΔABC की भुजाएं हैं, तो 2S = a + b + c है।
⇒ 2S = 18 + 24 + 30 = 72
⇒ S = 36
चूँकि हम जानते हैं कि,\(\sin \frac{A}{2} = \sqrt {\frac{{\left( {S - b} \right)\left( {S - C} \right)}}{{bc}}} \)
\(\Rightarrow \sin \frac{A}{2} = \sqrt {\frac{{\left( {36 - 24} \right) \times \left( {36 - 30} \right)}}{{24 \times 30}}} = \frac{1}{{\sqrt {10} }}\)
अतः विकल्प A सही उत्तर है।
Last updated on Jun 11, 2025
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