Answer:
D. [tex] x = \frac{5*\sqrt{2}}{2} [/tex]
Step-by-step explanation:
Reference angle = 45°
Length of Opposite side = x
Hypotenuse length = 5
Applying trigonometric ratio, we have:
[tex] sin(45) = \frac{x}{5} [/tex]
Multiply both sides by 5
[tex] 5*sin(45) = \frac{x}{5}*5 [/tex]
[tex] 5*sin(45) = x [/tex]
[tex] 5*\frac{1}{\sqrt{2}} = x [/tex] (sin 45 = 1/√2)
[tex] \frac{5}{\sqrt{2}} = x [/tex]
Rationalize
[tex] \frac{5*\sqrt{2}}{\sqrt{2}*\sqrt{2}} = x [/tex]
[tex] x = \frac{5*\sqrt{2}}{2} [/tex]
