Answer:
a = [tex]\frac{2}{3}[/tex] [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{3a}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
3a = 2[tex]\sqrt{2}[/tex] ( divide both sides by 3 )
a = [tex]\frac{2}{3}[/tex] [tex]\sqrt{2}[/tex]
