Answer: a. [tex]\dfrac{5\sqrt{2}}{2}[/tex]
Step-by-step explanation:
In the given picture we have aright triangle with Length of Hypotenuse = 5 units.
By using trigonometric ratios , we have
[tex]\sin\theta=\dfrac{\text{side opposite to }\theta}{\text{Hypotenuse}}\\\\\Rightarrow\sin45^{\circ}=\dfrac{x}{5}\ \ [\because \sin 45^{\circ}=\dfrac{1}{\sqrt{2}}]\\\\\Rightarrow\ \dfrac{1}{\sqrt{2}}=\dfrac{x}{5}\\\\\Rightarrow\ x=\dfrac{5}{\sqrt{2}}[/tex]
Rationalize : [tex]x=\dfrac{5}{\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{5\sqrt{2}}{2}[/tex]
Hence, the value of x = [tex]\dfrac{5\sqrt{2}}{2}[/tex]
