Question

In \( \triangle ABC \), given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find \( c \).

• A. 2
• B. 4
• C. 6
• D. 8

Hint:

Use the Cosine Rule: \( c^2 = a^2 + b^2 - 2ab \cos C \).

Answer 1

The Correct Option is D

Using the Cosine Rule: \[ c^2 = a^2 + b^2 - 2ab \cos C \] Substituting the values: \[ c^2 = 26^2 + 30^2 - 2(26)(30) \left(\frac{63}{65}\right) \] \[ = 676 + 900 - 1560 \times \frac{63}{65} \] \[ = 1576 - \frac{98280}{65} \] \[ = 1576 - 1512 = 64 \] \[ c = \sqrt{64} = 8 \] Thus, the correct answer is \( 8 \).