Question

From the following figure, it is given:
$\sin A$ is $\frac{\sqrt{m}}{2}$,

m is?

Answer 1

Given, $△ABC$, $\angle ABC={90}^{\circ }$, $AB=BC=a$
By Pythagoras Theorem,
$A{C}^2=A{B}^2+B{C}^2$
$A{C}^2=a^2+a^2$
$AC=a\sqrt{2}$
Now, $\sin A=\frac{P}{H}=\frac{BC}{AC}=\frac{a}{a\sqrt{2}}=\frac{\sqrt{2}}{2}$