Answer: The value of the variable is [tex]x=\dfrac{5\sqrt2}{2}.[/tex]
Step-by-step explanation: We are given to find the value of the variable 'x' in the figure.
We can see that the figure is a right-angled triangle with the length of the hypotenuse as follows:
h = 5 units.
Now, with respect to the angle of measure 45°, the length of the perpendicular is x units.
That is, p = x units.
From relations between trigonometric ratios, we have
[tex]\sin 45^\circ=\dfrac{\textup{perpendicular}}{\textup{hypotenuse}}\\\\\\\Rightarrow \dfrac{1}{\sqrt2}=\dfrac{p}{h}\\\\\\\Rightarrow \dfrac{1}{\sqrt2}=\dfrac{x}{5}\\\\\\\Rightarrow x=\dfrac{5}{\sqrt2}\\\\\\\Rightarrow x=\dfrac{5\sqrt2}{(\sqrt2)^2}\\\\\\\Rightarrow x=\dfrac{5\sqrt2}{2}.[/tex]
Thus, the value of the variable is [tex]x=\dfrac{5\sqrt2}{2}.[/tex]
