Question

If angles A, B, C of a ΔABC form an increasing AP, then sin B =
A. 1/2
B. √3/2
C. 1
D. 1/√2

Answer 1

B. √3/2

Step-by-step explanation:

Sum of all angles of triangle = 180

So A + B + C = 180

Given: A, B, C are in AP

Let us assume the difference is d.

So B and C can be written as A +d and A + 2d.

A + B + C = 180

A + A +d + A + 2d = 180

3A +3d = 180

A + d = 180/ 3 = 60

So B = 60

Sin B = Sin 60 = √3/2

Option B is the answer.