In a ∆ABC, if sin2A + sin2B = sin2C, show that the triangle is right – InterviewSolution

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1.

In a ∆ABC, if sin2A + sin2B = sin2C, show that the triangle is right-angled.

Answer»

Given:sin²A + sin²B = sin²C

To prove: The triangle is right-angled

sin²A + sin²B = sin²C

We know, a/sinA = b/sinB = c/sinC = 2R

So,

sin²A + sin²B = sin²C

a²/4R² + b²/4R² = c²/4R²

a² + b² = c²

This is one of the properties of right angled triangle. And it is satisfied here. Hence, the triangle is right angled. [Proved]

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