Question : If $\triangle \mathrm{ABC}$ is right angled at $B, A B = 12 \mathrm{~cm},$ and $\angle \mathrm{CAB} = 60^{\circ}$, determine the length of BC.
Option 1: $12 \sqrt{2} \mathrm{~cm}$
Option 2: $12\mathrm{~cm}$
Option 3: $12 \sqrt{3} \mathrm{~cm}$
Option 4: $24 \sqrt{3} \mathrm{~cm}$
Correct Answer: $12 \sqrt{3} \mathrm{~cm}$
Solution :
Given: AB = 12 cm
AC is the hypotenuse of the triangle.
We have to find tan of $\angle CAB = \tan 60° = \frac{\text{BC}}{\text{AB}}$
$⇒\sqrt{3} = \frac{\text{BC}}{12}$
$\therefore\text{BC} = 12\sqrt{3}\mathrm{~cm}$
Hence, the correct answer is $12\sqrt{3}\mathrm{~cm}$.
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