In a triangle ABC,if B=30​ degrees and c=root 3 b,then A can be equal to

We are given a triangle ABC where:

Angle B = 30°
Side c = √3 * b
We need to determine the possible value(s) of angle A.

Step 1: Use the Sine Rule
The Sine Rule states:

a / sin A = b / sin B = c / sin C

Substituting the given values:

b / sin 30° = (√3 * b) / sin C

Since sin 30° = 1/2, we get:

b / (1/2) = (√3 * b) / sin C
=> 2b = (√3 * b) / sin C

Dividing both sides by b (assuming b ≠ 0):

2 = (√3 / sin C)

Step 2: Solve for sin C
Rearranging for sin C:

sin C = √3 / 2

We know that sin 60° = √3 / 2, so:

C = 60°

Step 3: Find A using Angle Sum Property
In a triangle, the sum of angles is always 180°:

A + B + C = 180°
A + 30° + 60° = 180°
A = 180° - 90°
A = 90°

Conclusion
Thus, the possible value of A is 90°.