Trigonometry - 2 (HEIGHT AND DISTANCE) || Quantitative Aptitude || CAT 2021 || 16 October

A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 18 metres. From the top of the pole, the angle of elevation of the top of the tower and angle of depression of the foot of the tower are 60⁰ and 30⁰ respectively. Find the height of the tower.

A ladder is resting against a wall, the angle between the foot of the ladder and the wall is 45º and the foot of the ladder is 6.6 m away from the wall. The length of the ladder (in m) is:

Let A and B be two towers with same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 60° , respectively. The ratio of the heights of B and A is:

Asha and Suman’s mud forts have respective heights of 9 cm and 16 cm. If the tops of the fort are 25 cm apart from each other, then the distance (in cm) between two forts is:

Tops of two poles of height 45 m and 31 m are connected by a rope. The rope makes an angle with the horizontal whose tangent is 7/11. What is the distance between the two poles (in metres)?

A ladder is resting against a wall. The angle between the foot of the ladder and wall is 60⁰, and the foot of the ladder is 3.6 m away from the wall. The length of the ladder ( in m) is:

A man is standing on a platform of height h. From the point where man is standing, the angle of elevation of the top of the tower, which is at a distance of 45√3 m from the platform, is 60˚. If the height of the tower is 210 m, then what is the height of the platform?

As observed from the top of a lighthouse, 77√3 m above the sea level, the angle of depression of a yacht sailing towards it changes from 30° to 60°. The distance travelled by the yacht during the period of observation is:

The angle of depression of two cars situating at same side of a hill of height 96m are 30^° and 60° respectively. Find the distance between the cars? (Use √3 = 1.73 and calculate up to nearest integer)