Answer:
x = y = [tex]\frac{1}{2}[/tex] [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex]
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{\sqrt{5} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
2x = [tex]\sqrt{10}[/tex] ( divide both sides by 2 )
x = [tex]\frac{1}{2}[/tex] [tex]\sqrt{10}[/tex]
Since the base angles are 45° then the triangle is isosceles with both legs congruent , thus
x = y = [tex]\frac{1}{2}[/tex] [tex]\sqrt{10}[/tex]
