Question : Two men standing on the same side of a pillar, 75 metres high, observe the angles of elevation of the top of the pillar to be $30^{\circ}$ and $60^{\circ}$, respectively. The distance between the two men is:

Option 1: $100\sqrt{3}$ m

Option 2: $100$ m

Option 3: $50\sqrt{3}$ m

Option 4: $25\sqrt{3}$ m

Question : The angle of elevation of the top of the pillar from the foot and the top of a building 20 m high, are 60° and 30°, respectively. The height of the pillar is:

Option 1: $10$ m

Option 2: $10\sqrt{3}$ m

Option 3: $60$ m

Option 4: $30$ m

Question : If the angle of elevation of the sun decreases from $45^\circ$ to $30^\circ$, then the length of the shadow of a pillar increases by 60 m. The height of the pillar is:

Option 1: $60(\sqrt{3}+1)$ metres

Option 2: $30(\sqrt{3}–1)$ metres

Option 3: $30(\sqrt{3}+1)$ metres

Option 4: $60(\sqrt{3}–1)$ metres

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 : From a point on a bridge across the river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$, respectively. If the bridge is at a height of 2.5 m from the banks, then the width of the river is: Take ($\sqrt{3}$ = 1.732).

Option 1: 5.83 metres

Option 2: 6.83 metres

Option 3: 5.76 metres

Option 4: 6.87 metres