Answer:(i) the other two sides are 6 and 6[tex]\sqrt{2}[/tex](ii) the other two sides are [tex]\frac{4}{3} and \frac{8}{3}[/tex]Step-by-step explanation:(i) Sine: sin(θ) = Opposite ÷ Hypotenuse Cosine: cos(θ) = Adjacent ÷ Hypotenuse Tangent: tan(θ) = Opposite ÷ AdjacentHere adjacent side = 6opposite side = dangle = 45°other angles are 90° and 45°tan (45) = Opposite ÷ Adjacent 1 = d ÷ 6∴ d = 6 × 1 = 6so opposite side = 6Hypotenuse ² = opposite side ² + adjacent side² = 6² + 6² = 36 + 36 = 72 hypotenuse = [tex]\sqrt{72}[/tex] = 6[tex]\sqrt{2}[/tex]the other two sides are 6 and 6[tex]\sqrt{2}[/tex](ii) here adjacent side = 4√3angle = 30°other angles are 90° and 60°opposite side = dtan ( 30) = opposite ÷ adjacent [tex]\frac{1}{\sqrt{3}}[/tex] = d ÷ 4√3[tex]\frac{1}{\sqrt{3}}[/tex] = d × ([tex]\frac{\sqrt{3}}{4}[/tex]) 3 d = 4therefore d = [tex]\frac{4}{3}[/tex]therefore opposite side = [tex]\frac{4}{3}[/tex]Hypotenuse ² = opposite side ² + adjacent side² =( [tex]\frac{4}{3}[/tex])² +( [tex]\frac{4}{\sqrt{3}}[/tex])² = [tex]\frac{64}{9}[/tex]therefore hypotenuse = [tex]\sqrt{\frac{64}{9}}[/tex] =[tex]\frac{8}{3}[/tex]the other two sides are [tex]\frac{4}{3} and \frac{8}{3}[/tex]