Question : $ABC$ is a right-angled triangle, right-angled at B and $\angle A=60°$ and $AB=20$ cm, then the ratio of sides $BC$ and $CA$ is:
Option 1: $\sqrt{3}:1$
Option 2:
$1:\sqrt{3}$
Option 3:
$\sqrt{3}:\sqrt{2}$
Option 4:
$\sqrt{3}:2$
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Correct Answer:
$\sqrt{3}:2$
Solution :
Given: $ABC$ is a right-angled triangle, right-angled at $B$.
$\angle A=60°$ and $AB=20$ cm
So, $\angle C=180°-90°-60°= 30°$
⇒ $\frac{BC}{CA}=\cos C$
⇒ $\frac{BC}{CA}=\cos 30°$
⇒ $\frac{BC}{CA}=\frac{\sqrt{3}}{2}$
⇒ $BC:CA=\sqrt{3}:2$
Hence, the correct answer is $\sqrt{3}:2$.
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