A straight tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. The height of the tree is :

1. $10(\sqrt{3} + 1)$ m

2. $10\sqrt{3}$ m

3. $10(\sqrt{3} - 1)$ m

4. $\Big(\dfrac{10}{\sqrt{3}}\Big)$ m

A person of height 2 m wants to get a fruit which is on a pole of height $\Big(\dfrac{10}{3}\Big)$ m. If he stands at a distance of $\Big(\dfrac{4}{\sqrt{3}}\Big)$ m from the foot of the pole, then the angle at which he should throw the stone so that it hits the fruit is:

1. 15°

2. 30°

3. 45°

4. 60°

From the foot of a tower, the angle of elevation of the top of a column is 60° and from the top of the tower, which is 25 m high, the angle of elevation is 30°. The height of the column is:

1. 14.4 m

2. 37.5 m

3. 42.5 m

4. 43.3 m

An observer standing 72 m away from a building notices that the angles of elevation of the top and the bottom of a flagstaff on the building are respectively 60° and 45°. The height of the flagstaff is:

1. 52.7 m

2. 73.2 m

3. 98.3 m

4. 124.7 m