Question

In right-angled triangle ABC, $\angle A={45}^{\circ }$, The ratio of AB : AC : BC will be equal to

• A. $1:1:\sqrt{2}$
• B. $\sqrt{2}:1:1$
• C. $1:\sqrt{2}:1$
• D. $1:1:1$

Answer 1

The correct option is C

$1:\sqrt{2}:1$

Angle of triangle are ${45}^{\circ },{45}^{\circ },{90}^{\circ }$, hence corresponding side will be in ratio $1:1:\sqrt{2}$.

$\begin{array}{ccccc}{45}^{\circ }& & {45}^{\circ }& & {90}^{\circ }\\ 1& :& 1& :& \sqrt{2}\\ \downarrow & & \downarrow & & \downarrow \\ AD& & BC& & AC\end{array}$