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: $10\sqrt{3}$ metres

Option 3: $10(2+\sqrt{3})$ metres

Option 4: $10(2-\sqrt{3})$ metres

Question : The top of a broken tree touches the ground at a distance of 15 metres from its base. If the tree is broken at a height of 8 metres from the ground, then the actual height of the tree is:

Option 1: 17 metres

Option 2: 20 metres

Option 3: 25 metres

Option 4: 30 metres

Question : The angle of depression of two ships from the top of a lighthouse is ${60}^{\circ }$ and ${45}^{\circ }$ towards the east. If the ships are 300 metres apart, the height of the lighthouse (in metres) is:

Option 1: $200(3+\sqrt{3})$

Option 2: $250(3+\sqrt{3})$

Option 3: $150(3+\sqrt{3})$

Option 4: $160(3+\sqrt{3})$

Question : The shadow of a tower when the angle of elevation of the sun is 45°, is found to be 10 metres longer than when it was 60°. The height of the tower is:

Option 1: $5\sqrt{3}-1$ metres

Option 2: $5(3+\sqrt{3})$ metres

Option 3: $10(\sqrt{3}-1)$ metres

Option 4: $10(\sqrt{3}+1)$ 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 : On the ground, there is a vertical tower with a flagpole on its top. At a point 9 metres away from the foot of the tower, the angles of elevation of the top and bottom of the flagpole are 60° and 30°, respectively. The height of the flagpole is:

Option 1: $5\sqrt{3}$ metres

Option 2: $6\sqrt{3}$ metres

Option 3: $6\sqrt{2}$ metres

Option 4: $6\sqrt{5}$ metres