Answer:
a = 6 units
[tex]c= 6\sqrt{2}\ units[/tex]
Step-by-step explanation:
Given:
Let Labelled the diagram first
Δ ABC right angle at ∠ C = 90°
∠ B = 45 °
AB = c
BC = a
AC = 6
To 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 units
Now for c we use Pythagoras theorem
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Substituting the given values we get
c² = a² + 6²
c² = 6² + 6²
c² = 36 + 36
c² = 72
∴ c = ±√72
as c cannot be negative
∴ [tex]c = 6\sqrt{2}\ units\\[/tex]
a = 6 units
[tex]c= 6\sqrt{2}\ units[/tex]
