Answer:
4
Step-by-step explanation:
Since the triangle is isosceles then the legs are congruent.
Using the sine ratio in the right triangle and
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then
sin45° = [tex]\frac{leg}{hypotenuse}[/tex] = [tex]\frac{leg}{4\sqrt{2} }[/tex]
Multiply both sides by 4[tex]\sqrt{2}[/tex]
sin45° × 4[tex]\sqrt{2}[/tex] = leg, that is
[tex]\frac{1}{\sqrt{2} }[/tex] × 4[tex]\sqrt{2}[/tex], hence
leg = 4
