Question

In a right angled triangle, if one angle is ${45}^o$ and the side opposite to it is K times the hypotenuse, then the value of K is

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

Answer 1

The correct option is C $\frac{1}{\sqrt{2}}$

Let the hypotenuse be $AC=x$

Now given $AB=Kx$

In $△ABC$

$\sin {45}^{\circ }=\frac{AB}{AC}$

$\frac{1}{\sqrt{2}}=\frac{Kx}{x}K=\frac{1}{\sqrt{2}}$