MULTIPLE CHOICE QUESTIONS: (MCQ’s)
1.If the length of the shadow of a tree is decreasing then the angle of elevation is___
(a) Increasing
(b) Decreasing
(c) Remains the same
(d) None of the above
2.The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is___
(a) 10 m
(b) 30/√3 m
(c) √3/10 m
(d) 30 m
3.If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building_____
(a) Increases
(b) Decreases
(c) Does not change
d) None of the above
4. If a tower 6m high casts a shadow of 2 √3 m long on the ground, then the sun’s
elevation is_______
(a) 60°
(b) 45°
(c) 30°
(d) 90°
5.The angle formed by the line of sight with the horizontal when the point is below the horizontal level is called: ______
(a) Angle of elevation
(b) Angle of depression
(c) No such angle is formed
(d) None of the above
6.The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called______
(a) Angle of elevation
(b) Angle of depression
(c) No such angle is formed
(d) None of the above
7.From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower standing straight is______
(a) 15√3
(b) 10√3
(c) 12√3
(d) 20√3
8.The line drawn from the eye of an observer to the point in the object viewed by the observer is said to be ______
(a) Angle of elevation
(b) Angle of depression
(c) Line of sight
(d) None of the above
9.The height or length of an object or the distance between two distant objects can be determined with the help of_____
(a) Trigonometry angles
(b) Trigonometry ratios
(c) Trigonometry identities
(d) None of the above
10 . AB is a tower and AC is called the _____ if ∠A = angle of elevation
(a) line of tower
(b) line of elevation
(c) line of sight
(d) slant line
11. If tan 30 = 1/√3 and AB = 10cm and tan 30 = AB/AC so AC = ____
(a) √3/10
(b) 10/√3
(c) 10√3
(d) none of the above
12. From a point on the ground which is 10m away from the foot of the tower. the angle of elevation of the top of the tower is 30 degree
find the height of tower we will solve using____
(a) tan 30
(b) tan 60
(c) sin 30
(d) cos 30
13. PD = 8/√2−1 = _____ (after rationalisating the denominator)
(a) 4 (√2 − 1)
(b) 8 (√2 + 1)
(c) 4 (√2 + 1)
(d) 8 (√2 − 1)
14. A kite is flying at a height of 90m above the ground. BC is the length of strip it makes an angle of 30 with the ground the length of the strip is ____
(a) 90 m
(b) 60 m
(c) 20√3
(d) 45 m
15. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower is 30°. The distance of the car from the base of tower (in m) is_____
(a) 25√3
(b) 50√3
(c) 75√3
(d) 150
16. A man at the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance travelled by the car during this time interval is_____
(a) 10√3 m
(b) 100√3/3 m
(c) 200√3/3 m
(d) 200√3 m
17. The angle of elevation of the top of a 15 m high tower at a point 15 m away
from the base of tower is_____
(a) 30°
(b) 60°
(c) 45°
(d) 75°
18. Two poles are 25 m and 15 m high and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is______
(a) 5 m
(b) 8 m
(c) 9 m
(d) 10 m
19. A ladder makes an angle of 60° with the ground, when placed along a wall. If the foot of ladder is 8 m away from the wall, the length of ladder is_________
(a) 4 m
(b) 8 m
(c) 8√2 m
(d) 16 m
20. At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is_______
(a) 30°
(b) 60°
(c) 90°
(d) 45°
Answers. + Clues.
1) : (a) ⇒ Draw and check.
2): (b) ⇒ Tan 30° = x/30
3) : (c) ⇒ Since height of building and the distance from the building both are increased there will be no change in angle of elevation.
4 ): (a) ⇒ 6/ 2√3 = √3 and tan 60° = √3
5) : (b) ⇒ Text book (9.2)
6) : (a) ⇒ Text book (9.2)
7) : (a) ⇒ Tan 60° = x/15
8) : (c) ⇒ Text book (9.2)
9) : (b) ⇒ Text book
10) : (d) ⇒ Text book
11) : (c) ⇒ put the value and solve
12) : (b) ⇒ rationalise and solve
13) : (c) ⇒ the angle that is got when the observer views is from above
14) : (d ) ⇒ draw the fig and then use sin 30
15) : (c) ⇒ Use Tan 30° = 75/x
16) : (c) ⇒ Use tan 30° = 100/x and tan 60° =100/y. Find x and y and subtract them
17) : (c) ⇒ As tan 45° = 1 and 15/15 = 1
18) : (d) ⇒ 25 −15 = 10 and tan 45° = 10/x
19) : (d) ⇒ Cos 60° = 8/x .Find x
20) : (d) ⇒ Tan(y°) = x/x = 1. S0 y = ?