Question

In \(△ABC\), with usual notations, if \(cosA = \frac{1}{2},a = 3,\angle B = \frac{π^c}{6}\), then the values of \(b\) and \(c\) are.....

• A. \(b = \sqrt{3},c = \sqrt{3}\)
• B. \(b = 2\sqrt{3},c = \sqrt{3}\)
• C. \(b = \sqrt{3},c = 2\sqrt{3}\)
• D. \(b = \sqrt{3},c = \frac{1}{\sqrt{3}}\)

Hint:

Find angle $A$, then $C$, then use the sine rule.

Answer 1

The Correct Option is C

Step 1: Use the right angle
$C=90^{\circ}$, so $c$ is the hypotenuse. $a=c\sin A$, so $c=\frac{3}{\sqrt3/2}=2\sqrt3$.
Then $b=c\sin B=2\sqrt3\times\frac12=\sqrt3$. Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C)}} \]