Answer:
x = y = 15[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{30}[/tex] ( multiply both sides by 30 )
30 × sin45° = x , then
x = 30 × [tex]\frac{\sqrt{2} }{2}[/tex] = 15[tex]\sqrt{2}[/tex]
The triangle is a right isosceles triangle thus the legs are congruent, then
x = y = 15[tex]\sqrt{2}[/tex]
