UPSC NDA Math Model Paper 8

Here, A, B and C are in AP
So, 2B = A + C
And sum of angles of triangle, A + B + C = 180°
⇒ 2B + B = 180
⇒ 3B = 180
⇒ B = 60°
Now, by sine rule,

sin‌A

a

=

sin‌B

b

⇒

b

a

=

sin‌B

sin‌A

⇒

√3

1

=

sin‌60°

sin‌A

⇒sin‌A=(√3∕2)×(1∕√3)
⇒ sin A = 1/2
⇒ A = 30°
Hence, option (1) is correct.