Question

If $a = 2$, $b = 3$, $c = 4$ in a triangle $ABC$, then $\cos C =$

• A. $\dfrac{1}{4}$
• B. $-\dfrac{1}{4}$
• C. $\dfrac{1}{2}$
• D. $-\dfrac{1}{2}$

Hint:

The Cosine Rule is very effective when three sides of a triangle are known.

Answer 1

The Correct Option is B

Apply Cosine Rule: $\cos C = \dfrac{a^2 + b^2 - c^2}{2ab}$
Substitute: $a = 2$, $b = 3$, $c = 4$
$\cos C = \dfrac{4 + 9 - 16}{2 \cdot 2 \cdot 3} = \dfrac{-3}{12} = -\dfrac{1}{4}$