Answer:
X = Y
Step-by-step explanation:
[tex]\huge {\boxed {\sf A+B+C = 180^o }}[/tex]
[tex]\huge {\boxed {\sf A+45^o+90^o = 180^o }}[/tex]
[tex]\huge {\boxed {\sf A+135^o = 180^o }}[/tex]
[tex]\huge {\boxed {\boxed {\bf A=45^o }}}[/tex]
- Now we must know the hypotenuse, knowing that:
[tex]\huge {\boxed {\blue {\sf \cfrac{a}{sin (A) } = c }}}[/tex]
So....
[tex]\huge {\text {$ \sf \cfrac{x}{sin \: 45^o } = \cfrac{x}{\frac{\sqrt{2} }{2} } = x \cdot \cfrac{2}{\sqrt{2} } = \cfrac{\sqrt{2} }{y } = 2x $}}[/tex]
Remembering that:
[tex]\huge {\boxed {\sf \bf sin \: 45^o = \cfrac{a}{a\sqrt{5} } = \cfrac{1 }{\sqrt{2} } = \cfrac{\sqrt{2} }{2} }}[/tex]
So:
[tex]\huge {\boxed {\sf \bf y = 2}}[/tex]
- I think that's it, good studies
