Question

$ABC$ is an isosceles right-angled triangle. Assuming $AB=BC=x$, find the value of each of the following trigonometric ratios:

$\sin {45}^0$ is $\frac{1}{\sqrt{2}}$
If true then enter $1$ and if false then enter $0$

Answer 1

Given: $△ABC$, $AB=BC=x$, $\angle ABC={90}^{\circ }$
By Pythagoras Theorem,
$A{C}^2=A{B}^2+B{C}^2$
$A{C}^2=x^2+x^2$
$A{C}^2=2x^2$
$AC=\sqrt{2}x$
Since, $AB=BC$, then by Isosceles triangle property,
$\angle ACB=\angle CAB={45}^{\circ }$
Now, $Sin{45}^{\circ }=SinC=\frac{AB}{AC}=\frac{x}{x\sqrt{2}}=\frac{1}{\sqrt{2}}$