Question

In \(\triangle ABC, \angle B = 90^\circ\). If \(\frac{AB}{AC} = \frac{1}{2}\), then \(\cos C\) is equal to

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

Hint:

In right-angled triangles, use \(\cos \theta = \frac{\text{base}}{\text{hypotenuse}}\) with respect to the angle.

Answer 1

The Correct Option is B

In \(\triangle ABC, \angle B = 90^\circ\), and \[ \cos C = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{AB}{AC} \] Given: \[ \frac{AB}{AC} = \frac{1}{2} \] So, \[ \cos C = \frac{1}{2} \]