UPSC NDA Math Model Paper 1

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

A

2

=√

(S−b)(S−C)

bc

⇒sin‌

A

2

=√

(36−24)×(36−30)

24×30

=

1

√10

Hence, option A is the correct answer.