For this case we have that by definition of trigonometric relations of rectangular triangles, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. So:
[tex]Sin (45) = \frac {leg} {h}[/tex]
Where h is the hypotenuse.
[tex]\frac {\sqrt {2}} {2} = \frac {leg} {h}[/tex]
We cleared h:
[tex]h = \frac {2leg} {\sqrt {2}}[/tex]
We rationalize:
[tex]h = \frac {2leg} {\sqrt {2}} * \frac {\sqrt {2}} {\sqrt {2}}\\h = \frac {2 \sqrt {2} * leg} {2}\\h = \sqrt {2} * leg[/tex]
ANswer:
Option A
