Question : A man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retreats 36 m from the bank, he finds that the angle is 30°. The breadth of the river is:

Option 1: 15 metres

Option 2: 18 metres

Option 3: 16 metres

Option 4: 11 metres

Question : If the angle of elevation of the top of a pillar from the ground level is raised from 30° to 60°, the length of the shadow of a pillar of height $50\sqrt{3}$ metres will be decreased by:

Option 1: 60 metres

Option 2: 75 metres

Option 3: 100 metres

Option 4: 50 metres

Question : The upper part of a tree broken at a certain height makes an angle of 60° with the ground at a distance of 10 metres from its foot. The original height of the tree was:

Option 1: $20\sqrt{3}$ metres

Option 2: $10{\sqrt3}$ metres

Option 3: $10\left (2+{\sqrt3} \right)$ metres

Option 4: $10\left (2-{\sqrt3}\right)$ metres

Question : From the top of a 20 metres high building, the angle of elevation from the top of a tower is 60° and the angle of depression of its foot is at 45°, then the height of the tower is: $(\sqrt{3} = 1.732)$

Option 1: 45.46 metres

Option 2: 45.64 metres

Option 3: 54.64 metres

Option 4: 54.46 metres

Question : In $\triangle A B C, O$ is the point of intersection of the bisectors of $\angle B$ and $\angle A$. If $\angle B O C=108^{\circ}$, then $\angle B A O=$?

Option 1: 27°

Option 2: 40°

Option 3: 18°

Option 4: 36°