Answer:
x = y = 15[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the sine ratio and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{30}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
2x = 30[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
x = 15[tex]\sqrt{2}[/tex]
The triangle is isosceles (45- 45- 90) , then 2 legs are congruent, so
y = x = 15[tex]\sqrt{2}[/tex]
