Question : In triangle ABC, $\angle$ B = 90°, and $\angle$C = 45°. If AC = $2 \sqrt{2}$ cm then the length of BC is:
Option 1: 3 cm
Option 2: 2 cm
Option 3: 1 cm
Option 4: 4 cm
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Correct Answer: 2 cm
Solution : AC = $2 \sqrt{2}$ cm Also, $\angle$B = 90°, and $\angle$C = 45° Applying angle sum property in triangle ABC, $\angle$ A + $\angle$ B + $\angle$ C = 180° or, $\angle$A + 90° + 45° = 180° or, $\angle$A = 45° Since, $\angle$A = $\angle$C, $\triangle$ABC is an isosceles triangle with AB = BC. So, BC 2 = AB 2 = $\frac{(AC)^2}{2}=4$ cm [using Pythagoras theorem] ⇒ BC = 2 cm Hence, the correct answer is 2 cm.
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