AP EAMCET · Maths · Properties of Triangles
In a triangle, if \(b=5, c=6, \tan \frac{A}{2}=\frac{1}{\sqrt{2}}\), then \(a=\)
- A \(\sqrt{41}\)
- B \(\sqrt{21}\)
- C \(\sqrt{14}\)
- D \(8 \sqrt{6}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{41}\)
Step-by-step Solution
Detailed explanation
\(\because \cos A=\frac{1-\tan ^2 \frac{A}{2}}{1+\tan ^2 \frac{A}{2}}\) \(=\frac{1-\left(\frac{1}{\sqrt{2}}\right)^2}{1+\left(\frac{1}{\sqrt{2}}\right)^2}=\frac{1}{3}\) \(\cos A=\frac{b^2+c^2-a^2}{2 b c}\) \(\frac{1}{3}=\frac{(5)^2+(6)^2-a^2}{2(5)(6)}\)…
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