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AP EAMCET · Maths · Properties of Triangles

In a \(\triangle A B C\), if \(a=4, b=5\) and \(c=7\), then
\[
\sin \left(\frac{A}{2}\right)=
\]

  1. A \(\sqrt{\frac{3}{35}}\)
  2. B \(\sqrt{\frac{35}{3}}\)
  3. C \(\sqrt{\frac{2}{35}}\)
  4. D \(\sqrt{\frac{1}{35}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{\frac{3}{35}}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { (*) } a=4, b=5, c=7 \\ & \therefore \quad s=\frac{a+b+c}{2}=\frac{4+5+7}{2}=\frac{16}{2} \\ & s=8 \\ & \therefore \quad \sin \frac{A}{2}=\sqrt{\frac{(s-b)(s-c)}{b c}} \\ & =\sqrt{\frac{(8-5)(8-7)}{5 \times 7}}=\sqrt{\frac{3}{35}} \\ & \end{aligned}\)