In Triangle ABC, ∠A is a Right Angle and ∠B = 45°. Find BC. If your Answer is not an Integer, Leave it in Simplest Radical Form.
We will be using the Pythagoras Theorem to solve this.
Answer: If ∠A is a Right Angle and ∠B = 45°, then BC = x√2.
Let's solve this step by step.
Given that ∠A =90°, ∠B = 45°
By angle sum property of triangle, ∠A + ∠B + ∠C = 180°
⇒ ∠C = 45°
Sides opposite to equal angles are equal. So, let AB = AC = x
According to Pythagoras Theorem: AB2 + AC2 = BC2
BC2 = x2 + x2
BC2 = 2x2
BC = x√2