Given that there is a right-angled triangle having the two sides as x and y and the third side is 5 units.
Also one of the angles is 45 degrees.
Explanation -
Here we will use the trigonometric formulae taking into consideration the angle 45.
Then, we know
[tex]\begin{gathered} tan\theta=\frac{Perpendicular}{Base} \\ and\text{ cos}\theta=\frac{Base}{Hypotenuse} \\ Also\text{ tan45=1 and cos45=}\frac{1}{\sqrt{2}} \end{gathered}[/tex]
For a 45-degree angle, the base is y, the perpendicular is 5 and the hypotenuse is x.
Then,
[tex]\begin{gathered} tan45=\frac{5}{y} \\ 1=\frac{5}{y} \\ y=5 \\ and\text{ cos45=}\frac{y}{x} \\ \frac{1}{\sqrt{2}}=\frac{5}{x} \\ x=5\sqrt{2} \end{gathered}[/tex]
So the values of x and y are 5√2 and 5 respectively and hence the option C is correct.
Therefore the final answer is y = 5 and x = 5√2
