Question : If $\triangle ABC$ is right-angled at B, AB = 30 units and $\angle ACB=60°$, what is the value of AC?
Option 1: $20$ units
Option 2: $20\sqrt3$ units
Option 3: $40$ units
Option 4: $60$ units
Correct Answer: $20\sqrt3$ units
Solution :
$\triangle ABC$ is right-angled at B.
$\sin\theta$ = $\frac{\text{Perpendicular}}{\text{Hypotenuse}}$
⇒ $\sin 60°$ = $\frac{AB}{AC}$
⇒ $\frac{\sqrt{3}}{2} = \frac{30}{AC}$
⇒ AC = $\frac{60}{\sqrt{3}}$
$\therefore$ AC = $20\sqrt{3}$ units
Hence, the correct answer is $20\sqrt{3}$ units.
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