Multiple choice questions (MCQ) on Height and distance

1. A radio transmitter antenna of height 100 m stands at the top of a tall building. At a point on the ground, the angle of elevation of bottom of the antenna is 45° and that of top of antenna is 60°. What is the height of the building?

a. 100 m           b. 50 m             c. 50(√3+1) m                d. 50(√3-1) m


2. The angle of elevation of the top of an unfinished pillar at a point 150 m from its base is 30°. If the angle of elevation at the same point is to be 45°, then the pillar has to be raised to a height of how many meters?

a. 59.4 m          b. 61.4 m          c. 62.4 m          d. 63.4 m


3. A ladder 25 m long is leaning against a wall which is perpendicular to the level ground. The bottom of the ladder is 7 m from the base of the wall. If the top of the ladder slips down 4 m, how much will the bottom of the ladder slip?

a. 7 m               b. 8 m               c. 10 m             d. 15 m


4. The shadow of a pole 6 metre high is 15 metre long and at the same time the shadow of a tree is 25 metre long. What is the height of the tree?

a. 21 m             b. 10 m             c. 35 m             d. None of the above


5. Suppose the angle of elevation of the top of a tree at a point E due east of the tree is 60° and that at a point F due west of the tree is 30°. If the distance between the points E and F is 160 feet, then what is the height of the tree?

a. 40√3 feet                 b. 60 feet                      c. 40/√3 feet                  d. 23 feet


6. A ladder of 17 ft length reaches a window which is 15 ft above the ground on one side of the street. Keeping its foot at the same point the ladder is turned to the other side of the street and now it reaches a window 8 ft high. What is the width of the street?

a. 23 ft              b. 15 ft             c. 25 ft              d. 30 ft


7. A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man’s eye when at a distance of 60 m from the bottom of tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat assuming that it is running in still water?

a. 31.5 km/h                  b. 36.5 km/h                  c. 38.5 km/h                  d. 40.5 km/h


8. The angles of elevation of the top of a tower from two points situated at distances 36 m and 64 m from its base and in the same straight line and it are complementary. What is the height of the tower?

a. 50 m             b. 48 m             c. 25 m             d. 24 m


9. The length of shadow of a tree is 16 m when the angle of elevation of the sun is 60°. What is the height of the tree?

a. 8 m               b. 16 m             c. 16√3 m          d. 16/√3