Question

The sides of a triangle \( ABC \) are given by \( a = 3 \), \( b = 5 \), and \( c = 3 \). Then \( \cos A = \)

• A. \( \frac{2}{6} \)
• B. \( \frac{1}{6} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{5}{6} \)

Hint:

Cosine Rule}
\( \cos A = \frac{b^2 + c^2 - a^2}{2bc} \)
Use carefully when angle is opposite to side \( a \)
Helps in angle calculation without trigonometric tables

Answer 1

The Correct Option is D

Use cosine rule: \[ \cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{5^2 + 3^2 - 3^2}{2 \cdot 5 \cdot 3} = \frac{25 + 9 - 9}{30} = \frac{25}{30} = \frac{5}{6} \]