Question

In a \(\triangle ABC\), \(a = 1, b = \sqrt{3}\) and \(\angle C = \frac{\pi}{6}\). Then the measure of the third side \(c =\)

• A. \(4\)
• B. \(3\)
• C. \(1\)
• D. \(2\)

Hint:

Whenever two sides and the included angle of a triangle are given, the cosine rule is the fastest and most direct method to find the third side: \[ c^2=a^2+b^2-2ab\cos C \] Always substitute standard trigonometric values like \[ \cos30^\circ=\frac{\sqrt3}{2} \] carefully to avoid arithmetic mistakes.

Answer 1

The Correct Option is C