In $\triangle ABC$ if $\sin^2 A + \sin^2 B = \sin^2 C$ then prove that the triangle is a right angled triangle.

In triangle ABC if sin² A + sin² B = sin² C then prove that the triangle is a right angled triangle.

Miscellaneous Exercise 3 · Q113

\triangle ABC

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By the Sine Rule, $a=k\sin A,b=k\sin B,c=k\sin C$ . Dividing the given equation by $k^2$ is the same as writing it directly in terms of sides: $a^2+b^2=c^2$ . By the converse of Pythagoras' theorem (or directly via the Cosine Rule: $\cos C=\dfrac{a^2+b^2-c^2}{2ab}=\dfrac{0}{2ab}=0\implies …

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Q.In $\triangle ABC$ if $\sin^2 A + \sin^2 B = \sin^2 C$ then prove that the triangle is a right angled triangle.

Concept understanding — Solving a Triangle - Sine Rule

Q.In △ABC\triangle ABC△ABC if sin⁡2A+sin⁡2B=sin⁡2C\sin^2 A + \sin^2 B = \sin^2 Csin2A+sin2B=sin2C then prove that the triangle is a right angled triangle.

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Q.In $\triangle ABC$ if $\sin^2 A + \sin^2 B = \sin^2 C$ then prove that the triangle is a right angled triangle.

Unlock everything free for 14 days