SEE (Unit – 16) Trigonometry Height and Distance (Exercise with Answers)

Trigonometry

Height and Distance- Part 1

Angle of elevation:

Whenever we see the objects which are higher than our level of eyes, we have to bend our head backwards and our eyes get rotated upwards in the anticlockwise direction. The straight line joining our right eyes to the point of the object at which our eyes are focusing is called the line of eyes is left sight or observation. The angle made by this line of sight with the horizontal line through the level of our eyes is called the angle of elevation.

Angle of depression:

Whenever we see an object at a lower height than the level of our eyes, we bend our head downwards and our eyes get rotated downwards in the clock wise direction. At this time, the angle made by the line of observation with the horizontal line through the level of angle of elevation our eyes is called the angle of depression.

Questions and Solutions:

1.    The top of a telegraph post is attached to a horizontal plane at a distance of 30m from the foot of the post. If the angle of elevation of the post is 30 ̊ from that point, find the height of the post.

2.    The top of a house which is 40√3m high is observed from a point on the horizontal ground 40m away from the base of the house. What will be the angle of elevation of the house?

3.    A tree of the height 25√3m is situated on the edge of a river. If the angle of elevation of the tree observed from the opposite edge of the river is found to be 60 ̊, what will be the breadth of the river?

4.    The bottom of a house which is 20√3m high, is observed from the roof of the opposite house 60m away from that house. Find the angle of depression if both of the houses have same height.

5.    A pigeon on the ground is observed from the roof of a house, which is 40m high. If the pigeon is 40√3m away from the bottom of the house on the ground, find the angle of depression of the pigeon from the observer.

6.    A 5ft tall person observed the top of a tower of 55 ft high from a point 50 ft away from the bottom of the tower on the horizontal level. Find the angle of elevation of that tower.

7.    An electric pole is erected at the centre of a circle of radius 10m. If the angle of elevation of the top of the pole is observed to be 60°from the circumference of the circle, what will be the height of the pole?

8.    The shadow of a vertical pole of height 30√3m is found to be 90m at 4Pm. What will be the angle of inclination (elevation) of the sun at that time?

9.    A pigeon on the roof of a house is observed from the top of a tower of height 120m at an angle of 30° to the horizontal line. Find the height of the house if the distance between the tower and the house is 60√3m.

10. A tall tree breaks because of a strong wind. If 30m long broken part of the tree meets the ground making 30̇ ̊ angle with the horizontal level, how tall was the tree and how far does it meet the ground level from the bottom of the tree?