Question

In an isosceles triangle ABC, if AC=BC and AB2=2AC2 then
angle B is?

Answer 1

Answer:

In an isosceles ∆ two sides are equal and the sides are AC=BC

if we take Angle C as 90° the ∆ will be a right isosceles ∆ and will also satisfy (AB)²=(AC)²+(BC)²

which is equal to (AB)²= (AC)²+(AC)² = 2(AC)² as AC and BC are equal.

So if AC = BC then the angles opposite to them which are Angle B and and Angle C respectively are equal.

So,

Angle A + Angle B + Angle C = 180°

[By Angle Sum Property Of ∆]

90°+Angle B+Angle A = 180°

90°+x+x=180°

(since Angle A = Angle B)

2x = 180°-90°

x=90°/2

x=Angle A = Angle B = 45°

therefore Angle B is 45°