Question:
In \( \triangle ABC \), if \( a, b, c \) are 5, 12, and 13 respectively, then \( b^2 \sin 2C + c^2 \sin 2B \) is:
In \( \triangle ABC \), if \( a, b, c \) are 5, 12, and 13 respectively, then \( b^2 \sin 2C + c^2 \sin 2B \) is:
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In right-angled triangles, use trigonometric identities and the sine rule to calculate expressions involving angles and sides.
Updated On: May 13, 2025
- 60
- 120
- 180
- 90
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The Correct Option is B
Solution and Explanation
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.
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