Question

Evaluate (5cos²60° + 4sec²30° – tan²45°)/(sin²30° + cos²30°)

In Figure 2, the angles of elevation of the top of a tower AB of height 'h' m, from two points P and Q at a distance of x m and y m from the base of the tower respectively and in the same straight line with it, are 60° and 30°, respectively. Prove that h² = xy.

The following TV Tower was built in 1988 and is located in Pitampura, Delhi. It has an observation deck. Observe the picture given below : The TV Tower stands vertically on the ground. From a point 'A' on the ground, the angle of elevation of top of the tower (point 'B') is 60°. There is a point 'C' on the tower which is 78 m (approx.) above the ground. The angle of elevation of the point C from point A is found to be 30°.

Qutub Minar, located in South Delhi, India, was built in the year 1193. It is 72 m high tower. Working on a school project, Charu and Daljeet visited the monument. They used trigonometry to find their distance from the tower. Observe the picture given below. Points C and D represent their positions on the ground in line with the base of tower, the angles of elevation of top of the tower (Point A) are 60° and 45° from points C and D respectively.

Two poles of equal heights are standing opposite each other on either side of the road of width 60 m. From a point P between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively, as shown in Figure 3. Find the height of the poles and distances of the point from the poles.