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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