Question : If $\triangle A B C$ is right angled at $B, A B=12 \mathrm{~cm}$ and $\angle C A B=60^{\circ}$, determine the length of $BC$.
Option 1: $24 \sqrt{3} \mathrm{~cm}$
Option 2: $12 \mathrm{~cm}$
Option 3: $12 \sqrt{2} \mathrm{~cm}$
Option 4: $12 \sqrt{3} \mathrm{~cm}$
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Correct Answer: $12 \sqrt{3} \mathrm{~cm}$
Solution :
Given, $\triangle$ABC is right angled at B, where AB = 12 cm and $\angle$CAB = 60°
By using the trigonometric ratio involving AB and BC.
To $\angle$CAB, AB is the adjacent side and BC is the opposite side.
$\tan\angle CAB$ = $\tan 60°$ = $\frac{BC}{AB}$
⇒ $\sqrt3=\frac{BC}{12}$
$\therefore BC =12\sqrt3\ \text{cm}$
Hence, the correct answer is $12\sqrt3\ \text{cm}$.
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