Question : A tower is broken at a point P above the ground. The top of the tower makes an angle of $60^\circ$ with the ground at Q. From another point R on the opposite side Q angle of elevation of point P is $30^\circ$. If QR = 180 m, what is the total height (in meters) of the tower?

Option 1: $90$

Option 2: $45\sqrt{3}$

Option 3: $45(\sqrt{3}+1)$

Option 4: $45(\sqrt{3}+2)$

Question : In $\triangle P Q R, S$ is a point on the side QR such that $\angle Q P S=\frac{1}{2} \angle P S R, \angle Q P R=78^{\circ}$ and $\angle P R S=44^{\circ}$. What is the measure of $\angle PSQ$?

Option 1: 68$^{\circ}$

Option 2: 56$^{\circ}$

Option 3: 58$^{\circ}$

Option 4: 64$^{\circ}$

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 : From point P on the level ground, the angle of elevation to the top of the tower is 30°. If the tower is 100 metres high, the distance of point P from the foot of the tower is: (Take $\sqrt{3}$ = 1.73)

Option 1: 149 m

Option 2: 156 m

Option 3: 173 m

Option 4: 188 m

Question : In $\triangle P Q R$, $\angle Q=90^{\circ}$, $PQ=8$ cm and $\angle P R Q=45^{\circ}$ Find the length of $QR$.

Option 1: 6 cm

Option 2: 3 cm

Option 3: 5 cm

Option 4: 8 cm

Question : From the top of an upright pole $24 \sqrt{3}$ feet high, the angle of elevation of the top of an upright tower was $60^{\circ}$. If the foot of the pole was 60 feet away from the foot of the tower, how tall (in feet) was the tower?

Option 1: $84 \sqrt{3}$

Option 2: $36\sqrt{3}$

Option 3: $44\sqrt{3}$

Option 4: $60\sqrt{3}$