In a ΔABC, if a = 18, b = 24 and c = 30 then find the value of sin (A/2) ?

CONCEPT:

If a, b and c are the sides of the Δ ABC such that, a + b + c = 2S then \(\sin \frac{A}{2} = \sqrt {\frac{{\left( {S - b} \right)\left( {S - C} \right)}}{{bc}}} \)

CALCULATION:

Given: For ΔABC we have a = 18, b = 24 and c = 30

Here, we have to find the value of  sin (A/2)

As we know that, if a, b and c are the sides of the Δ ABC then 2S = a + b + c

⇒ 2S = 18 + 24 + 30 = 72

⇒ S = 36

As we know that, \(\sin \frac{A}{2} = \sqrt {\frac{{\left( {S - b} \right)\left( {S - C} \right)}}{{bc}}} \)

\(\Rightarrow \sin \frac{A}{2} = \sqrt {\frac{{\left( {36 - 24} \right) \times \left( {36 - 30} \right)}}{{24 \times 30}}} = \frac{1}{{\sqrt {10} }}\)

Hence, option A is the correct answer.