Answer:
Θ = 45°
BA = [tex]3\sqrt{2}[/tex] = 4.243
Step-by-step explanation:
i) the given triangle is a right angled isosceles triangle.
ii) the base and the height are both equal. height = base = 3 cm.
iii) from the rule of triangles the sum of all angles in a triangle is 180° and since the triangle is an right angled isosceles triangle one angle is 90° and the other two angles are equal.
Therefore
Θ° + Θ° + 90° = 180° ⇒ 2Θ° = 180° - 90° = 90° ∴ Θ = 45°
iv) the hypotenuse BA is given by the Pythagoras' theorem
∴ hypotenuse (BA) = [tex]\sqrt{base^{2} + height^{2} }[/tex] = [tex]\sqrt{BC^{2} + CA^{2} }[/tex] = [tex]\sqrt{3^{2} + 3^{2} }[/tex] = [tex]3\sqrt{2}[/tex] = therefore BA = [tex]3\sqrt{2}[/tex] = 4.243
