Answer:
x = y = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] ( multiply both sides by 8 )
8 × cos45° = x , then
x = 8 × [tex]\frac{\sqrt{2} }{2}[/tex] = 4[tex]\sqrt{2}[/tex]
The third angle in the triangle = 45° ( sum of angles in triangle )
Then the triangle is isosceles with congruent legs, thus
x = y = 4[tex]\sqrt{2}[/tex]
