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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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.
Question : Suppose $\triangle A B C$ be a right-angled triangle where $\angle A=90^{\circ}$ and $A D \perp B C$. If area $(\triangle A B C)$ $=80 \mathrm{~cm}^2$ and $BC=16$ cm, then the length of $AD$ is:
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Question : $\triangle PQR$ is right-angled at $Q$. The length of $PQ$ is 5 cm and $\angle P R Q=30^{\circ}$. Determine the length of the side $QR$.
Question : $ABC$ is a triangle and $D$ is a point on the side $BC$. If $BC = 16\mathrm{~cm}$, $BD = 11 \mathrm{~cm}$ and $\angle ADC = \angle BAC$, then the length of $AC$ is equal to:
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