(A) Given sides are $a=4, b=5, c=7$. First,calculate the semi-perimeter $s$: $s = \frac{a+b+c}{2} = \frac{4+5+7}{2} = \frac{16}{2} = 8$. The formula f

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(A) Given sides are $a=4, b=5, c=7$. First,calculate the semi-perimeter $s$: $s = \frac{a+b+c}{2} = \frac{4+5+7}{2} = \frac{16}{2} = 8$. The formula for $\sin \left(\frac{A}{2}\right)$ is: $\sin \left(\frac{A}{2}\right) = \sqrt{\frac{(s-b)(s-c)}{bc}}$. Substituting the values: $\sin \left(\frac{A}{2}\right) = \sqrt{\frac{(8-5)(8-7)}{5 \times 7}} = \sqrt{\frac{3 \times 1}{35}} = \sqrt{\frac{3}{35}}$.

Class 11 Mathematics Trigonometrical Equations Relation between sides and angles, Solutions of triangles

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

AP EAMCET 2022 All AP EAMCET

A
$\sqrt{\frac{3}{35}}$
B
$\sqrt{\frac{35}{3}}$
C
$\sqrt{\frac{2}{35}}$
D
$\sqrt{\frac{1}{35}}$

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Relation between sides and angles, Solutions of triangles

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

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