UPSC NDA Math Model Paper 2

Given: For ΔABC we have a = 13, b = 14 and c = 15
Here, we have to find the value of tan (B/2)
As we know that, if a, b and c are the sides of the Δ ABC then 2S = a + b + c
⇒ 2S = 13 + 14 + 15 = 42
⇒ S = 21
As we know that, tan‌

B

2

=√

(S−c)(S−a)

S(S−b)

⇒tan‌

B

2

=√

(21−15)×(21−13)

21×7

=

4

7

Hence, option C is the correct answer.