UPSC NDA Math Model Paper 4

Given: For ΔABC we have a = 25, b = 52 and c = 63
Here, we have to find the value of sin (C/2)
As we know that, if a, b and c are the sides of the Δ ABC then 2S = a + b + c
⇒ 2S = 25 + 52 + 63 = 140
⇒ S = 70
As we know that, sin‌

C

2

=√

(S−a)(S−b)

ab

⇒sin‌

C

2

=√

(70−25)×(70−52)

25×52

=

9

√130

Hence, option B is the correct answer.