Question

In \( \triangle ABC \), if \( a, b, c \) are 5, 12, and 13 respectively, then \( b^2 \sin 2C + c^2 \sin 2B \) is:

• A. 60
• B. 120
• C. 180
• D. 90

Hint:

In right-angled triangles, use trigonometric identities and the sine rule to calculate expressions involving angles and sides.

Answer 1

The Correct Option is B

We are given the sides \( a = 5 \), \( b = 12 \), and \( c = 13 \) in \( \triangle ABC \). Step 1: Since \( 5^2 + 12^2 = 13^2 \), \( \triangle ABC \) is a right-angled triangle with \( \angle C = 90^\circ \). Step 2: Use the formula for the area of a right-angled triangle and the sine rule to find \( b^2 \sin 2C + c^2 \sin 2B \). Step 3: After simplifying, we get the final result as 120. Thus, the correct answer is 120.