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°

The distance between two multi-storeyed buildings is 60 m. The angle of depression of the first building as seen from the top of the second building, which is 150 m high, is 30°. The height of the first building is :

1. 115.36 m

2. 117.85 m

3. 125.36 m

4. 128.34 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

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and that of the top of the flagstaff is β. The height of the tower is :

1. $\Big(\dfrac{h \tan \beta}{\tan \beta - \tan \alpha}\Big)$

2. $\Big(\dfrac{h \sin \beta}{\tan \beta - \tan \alpha}\Big)$

3. $\Big(\dfrac{h \cot \alpha}{\cot \beta - \cot \alpha}\Big)$

4. $\Big(\dfrac{h \tan \alpha}{\tan \beta - \tan \alpha}\Big)$