Answer:
BC = 18
Step-by-step explanation:
Since ∠B = ∠C then the triangle is isosceles and so
∠B = ∠C = 45°
Using the sine ratio in the right triangle and
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{9\sqrt{2} }{BC}[/tex]
Multiply both sides by BC
BC × sin45° = 9[tex]\sqrt{2}[/tex], that is
BC × [tex]\frac{1}{\sqrt{2} }[/tex] = 9[tex]\sqrt{2}[/tex]
Multiply both sides by [tex]\sqrt{2}[/tex]
BC = 9[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 9 × 2 = 18
