Question:
In \( \triangle ABC \) with usual notations, \( a = 4 \), \( b = 3 \), \( \angle A = 60^\circ \), then \( c \) is a root of the equation
In \( \triangle ABC \) with usual notations, \( a = 4 \), \( b = 3 \), \( \angle A = 60^\circ \), then \( c \) is a root of the equation
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When sides and an included angle are given, always use the cosine rule to form the required equation.
Updated On: Mar 28, 2026
- \( c^2 - 3c - 7 = 0 \)
- \( c^2 - 3c + 7 = 0 \)
- \( c^2 + 3c - 7 = 0 \)
- \( c^2 + 3c + 7 = 0 \)
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The Correct Option is A
Solution and Explanation
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 \[ \boxed{c^2 - 3c - 7 = 0} \]
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 \[ \boxed{c^2 - 3c - 7 = 0} \]
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