If in a Δ ABC, perimeter is 12 units, b = 3 units, c = 5 units then find s i n ( A 2 ) . Options: A . &nbsp 1 √ 5 B . &nbsp √ 5 C . &nbsp 1 √ 3 D . &nbsp √ 3

If in a Δ ABC, perimeter is 12 units, b = 3 units, c = 5 units then find

Question -

If in a $Δ$ ABC, perimeter is 12 units, b = 3 units, c = 5 units then find $s i n (\frac{A}{2})$ .

Options:

A .

\frac{1}{\sqrt{5}}

B .

\sqrt{5}

C .

\frac{1}{\sqrt{3}}

D .

\sqrt{3}

Answer: Option A
:
A
We know,

s i n (\frac{A}{2}) = \sqrt{\frac{(s - b) (s - c)}{b . c}}

Where"s" is the semiperimeter and b & c are the sides of a triangle.
We'll do the appropriate substitution -

s i n (\frac{A}{2}) = \sqrt{\frac{(6 - 3) (6 - 5)}{3.5}}

s i n (\frac{A}{2}) = \frac{1}{\sqrt{5}}

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