Question

In a triangle $ABC$ given ${\sin }^{2}A+{\sin }^{2}B={\sin }^{2}C$, then the triangle is

• A. equilateral
• B. isosceles
• C. right-angled
• D. none of these

Answer 1

The correct option is C right-angled

Given In the triangle $ABC$ given ${\sin }^{2}A+{\sin }^{2}B={\sin }^{2}C$......(1).

We have for any triangle $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R$.....(2). [ Using sine rule for triangle $ABC$]

Using (2) in (1) we get,

$a^2+b^2=c^2$.

This is nothing but the pythagorous theorem and which is true only for right-angled triangle.

So the given triangle $ABC$ is right-angled.