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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 Angle Sum Theorem and the Pythagoras theorem to solve this.
Answer: If ∠A is a Right Angle and ∠B = 45°, then BC = AB√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
Since AB = x, therefore BC = AB√2
Hence, if ∠A is a right angle and ∠B = 45°, then BC = AB√2.