Determine the missing measures.38, a=

Answer:a = 6 units[tex]c= 6\sqrt{2}\ units[/tex]Step-by-step explanation:Given:Let Labelled the diagram firstΔ ABC right angle at ∠ C = 90°∠ B = 45 °AB = cBC = aAC = 6To Find: a =?c =?Solution:In Δ ABC∠ A + ∠ B + ∠ C = 180°.....{Angle Sum Property of a Triangle}∴ ∠ A + 45 + 90 = 180°∴ ∠ A = 180 - 135∴ ∠ A = 45°Now ∠ A = ∠ B = 45°  in Δ ABC∴ Δ ABC is an Isosceles Triangle.∴ Two sides are equal of an  Isosceles Triangle.∴ AC = BC = a = 6 unitsNow for c we use Pythagoras theorem[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]Substituting the given values we getc² = a² + 6²c² = 6² + 6²c² = 36 + 36c² = 72∴ c = ±√72as c cannot be negative∴ [tex]c = 6\sqrt{2}\ units\\[/tex]a = 6 units[tex]c= 6\sqrt{2}\ units[/tex]