Question

In \( \triangle ABC \) with usual notations, \( a = 4 \), \( b = 3 \), \( \angle A = 60^\circ \), then \( c \) is a root of the equation

• A. \( c^2 - 3c - 7 = 0 \)
• B. \( c^2 - 3c + 7 = 0 \)
• C. \( c^2 + 3c - 7 = 0 \)
• D. \( c^2 + 3c + 7 = 0 \)

Hint:

When sides and an included angle are given, always use the cosine rule to form the required equation.

Answer 1

The Correct Option is A

Step 1: Apply the cosine rule.
For triangle \( ABC \), \[ a^2 = b^2 + c^2 - 2bc \cos A \]

Step 2: Substitute the given values.
\[ 4^2 = 3^2 + c^2 - 2(3)(c)\cos 60^\circ \] \[ 16 = 9 + c^2 - 3c \]

Step 3: Rearrange the equation.
\[ c^2 - 3c - 7 = 0 \]

Step 4: Conclusion.
Hence, \( c \) satisfies the equation \[ \boxed{c^2 - 3c - 7 = 0} \]