Learn In Triangle Abc A Is A Right Angle And B45

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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.

**Explanation:**

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: AB^{2} + AC^{2} = BC^{2}

BC^{2} = x^{2} + x^{2}

BC^{2} = 2x^{2}

BC = x√2

Since AB = x, therefore BC = AB√2

### Hence, if ∠A is a right angle and ∠B = 45°, then BC = AB√2.

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