Answer:
x = y = 6.5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
the triangle is isosceles, both base angles are 45° then the 2 legs are congruent , that is x = y
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}{13}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
2x = 13[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
x = y = 6.5[tex]\sqrt{2}[/tex]
