Question

In triangle ABC, with usual notations, if \(a = 4,b = 5\) and \(c = 6\), then angle C is equal to...

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

Hint:

Find cos A and cos C by the cosine rule and compare cos 2A with cos C.

Answer 1

The Correct Option is B

Step 1: Use sine rule check
A triangle with $c^2 = a(a+b)$ has $C=2A$. Here $a(a+b) = 4\times9 = 36 = c^2$.

Step 2: Why this works
The relation $c^2 = a^2+ab$ is exactly the condition for $C = 2A$.

Step 3: Result
Option (B).

Final Answer:
C = 2A. \[ \boxed{\text{(B)}\ C = 2A} \]