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 $QR$.

Option 1: $5 \sqrt{3}~cm$

Option 2: $3 \sqrt{3}~cm$

Option 3: $\frac{1}{\sqrt{3}}~cm$

Option 4: $\frac{5}{\sqrt{3}}~cm$

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:

Option 1: 10 cm

Option 2: 24 cm

Option 3: 18 cm

Option 4: 12 cm

Question : In $\triangle$LMN, LM = $5\sqrt{2}$ cm, LN = 13 cm and $\angle$LMN=135$^{\circ}$. What is the length (in cm) of MN?

Option 1: $7$

Option 2: $8$

Option 3: $8\sqrt{2}$

Option 4: $7\sqrt{2}$

Question : In a right-angled triangle $\Delta PQR, PR$ is the hypotenuse of length 20 cm, $\angle PRQ = 30^{\circ}$, the area of the triangle is:

Option 1: $50\sqrt{3}\text{ cm}^{2}$

Option 2: $100\sqrt{3}\text{ cm}^{2}$

Option 3: $25\sqrt{3}\text{ cm}^{2}$

Option 4: $\frac{100}{\sqrt{3}}\text{ cm}^{2}$

Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is:

Option 1: 12 cm

Option 2: 18 cm

Option 3: 4 cm

Option 4: 6 cm