Question : In a triangle ABC, AB = 6$\sqrt{3}$ cm,  AC = 12 cm and BC = 6 cm. Then the measure of $\angle B$ is equal to:

Option 1: 90°

Option 2: 45°

Option 3: 70°

Option 4: 60°

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

Question : $\triangle ABC$ is an equilateral triangle with a side of 12 cm and AD is the median. Find the length of GD if G is the centroid of $\triangle ABC$.

Option 1: $6 \sqrt{3}$ cm

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

Option 3: $4 \sqrt{3} $ cm

Option 4: $2 \sqrt{3}$ cm

Question : In $\triangle{XYZ}$, right-angled at $Y$, if $\sin X = \frac{1}{2}$, find the value of $\cos X \cos Z + \sin X \sin Z$.

Option 1: $\frac{\sqrt{3}}{2}$

Option 2: $\frac{\sqrt{3}}{4}$

Option 3: $\frac{2}{\sqrt{3}}$

Option 4: $\sqrt{3}$

Question : In triangle ABC, $\angle$ B = 90°, and $\angle$C = 45°. If AC = $2 \sqrt{2}$ cm then the length of BC is:

Option 1: 3 cm

Option 2: 2 cm

Option 3: 1 cm

Option 4: 4 cm