CBSE Class 10 Mathematics Statistics Worksheet Set A

Question. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
(a) 20(√3 –1)m
(b) 20√3m
(c) 20 m
(d) 40 m

Answer: A

Question. The angles of elevation of the top of a tower, as seen from two points A and B situated in the same line and at distance x and y respectively. from the foot of the tower, are complementary. Find the height of the tower.
(a) √x+y
(b) √xy
(c) xy
(d) √x + √y

Answer: B

Question. A 15m long ladder placed vertically along a wall broke in such a way that its top touches the ground making an angle of 60° with it. At what height from the ground did the ladder break?
(a) 7.34 m
(b) 8 m
(c) 9.46 m
(d) 6.96 m

Answer: D

Question. A tree 6 m tall casts a 4 cm long shadow. At the same time, a flag pole casts a shadow 50 m long. How long is the flag pole?
(a) 75 m
(b) 100 m
(c) 150 m
(d) 50 m

Answer: A

Question. The height of a tower is h and the angle of elevation of the top of the twoer is α. On moving a distance h/2 towards the tower, the angle of elevation becomes β. What is the value of cotα – cotβ?
(a) 1/2
(b) 2/3
(c) 1
(d) 2

Answer: A

Question. A bridge across a river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, width of the river is
(a) 75√2m
(b) 150 m
(c) (75/√2) m
(d) 75 m

Answer: A

Question. A professor standing on one end of a football field observes the elevation of the top of a flood light tower at an angle of α. He then walks a distance equal to twice the height of the tower and finds that the elevation of the top is now at an angle of 90°– α. What is the value of tanα ?
(a) 1− √2
(b) √2 −1
(c) √2
(d) 1

Answer: B

Question. An electrician has a repair an electric fault on a pole of height 5 cm. He has to reach a point 1.3 m below the top of the pole to undertake the repair work. What shouldbe the length of the ladder that he should use which, when inclined at an angle of 60° to the horizontal, would enable him to reach the required position? Also, how far from the foot of the pole should he place the foot of the ladder? [Take √3 = 1.73].
(a) 4.28 m, 2.14 m
(b) 4.28 m, 2.83 m
(c) 4.6 7m, 2.14 m
(d) 3.67 m, 2.14 m

Answer: A

Question. An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively.Find the distance between the two planes at that instant.
(a) 3920 m
(b) 6250 m
(c) 5125 m
(d) 4444 m

Answer: B

Question. If the angle of depression of an object from a 75 m high tower is 30°, then the distance of the object from the tower is
(a) 25√3 m
(b) 50√ 3 m
(c) 75√3 m
(d) 150 m

Answer: C

Question. The angles of elevation of the top of a tower from two points at distances m and n metres are complementary. If the two points and the base of the tower are on the same straight line, then the height of the tower is
(a) √mn
(b) mn
(c) m/n
(d) None of these

Answer: A

Question. If the height and length of the shadow of a man are the same, then the angle of elevation of the sun is
(a) 45°
(b) 60°
(c) 90°
(d) 120°

Answer: A

Question. The height of a tree, if it casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45°, is
(a) 10 m
(b) 14 m
(c) 8 m
(d) 15 m

Answer: D

Question. A person walks towards a tower. Initially when he starts, angle of elevation of the top of tower is 30°. On travelling 20 metres towards the tower, the angle changes to 60°. How much more has he to travel to reach the tower?
(a) 10√3 metres
(b) 10 metres
(c) 20 metres
(d) (10/√3)metres

Answer: B

Question. ABC is a field in the form of an equilateral triangle. Two vertical poles of heights 45m and 20m are erected at A and B respectively. The angles of elevation of the tops of the two poles from C are complementary to each other. There is a point D on AB such that from it, the angles of elevation of the tops of the two poles are equal.Then AD is equal to –
(a) 17(5/12)m
(b) 20(10/13)m
(c) 20(5/13)m
(d) 17(10/12)m

Answer: B

Question. A vertical pole of height 10 metres stands at one corner of a rectangular field. The angle of elevation of its top from the farthest corner is 30º, while that from another corner is 60º. The area (in m²) of rectangular field is
(a) 200√2/3
(b) 400/√3
(c) 200√2/3
(d) 400√2/3

Answer: A

Question. From the top of a building of height ‘h’ meter, the angle of elevation of the top of the tower is ‘a’ and angle of depression of the foot of the tower is ‘b’. The height of the tower is
(a) h + (tanα + tanβ)/tanβ
(b) h (tanα + tanβ)/tanβ
(c) h + tan(α + β)/tanβ
(d) h tan(α + β)/tanβ

Answer: B

Question. Which of the following statements are incorrect?
(a) Line of sight is the line drawn from the eyes of the observer to a point in the object where the person is viewing.
(b) Angle of elevation is the angle formed by the line of sight with horizontal through the eyes of observer when the object is above the horizontal level.
(c) Angle of depression is the angle formed by the line of sight with the horizontal when the object is below the horizontal level.
(d) None of these

Answer: D

DIRECTIONS : Study the given Case/Passage and answer the following questions.

Case/Passage-I

A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919.The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 metres) in height.

Question. What is the angle of elevation if they are standing at a distance of 42m away from the monument?
(a) 30°
(b) 45°
(c) 60°
(d) 0°

Answer: B

Question. They want to see the tower at an angle of 60°. So, they want to know the distance where they should stand and hence find the distance.
(a) 25.24 m
(b) 20.12 m
(c) 42 m
(d) 24.64 m

Answer: A

Question. If the altitude of the Sun is at 60°, then the height of the vertical tower that will cast a shadow of length 20 m is
(a) 20√3 m
(b) 20/√3 m
(c) 15/√3 m
(d) 15√3 m

Answer: A

Question. The ratio of the length of a rod and its shadow is 1:1 . The angle of elevation of the Sun is
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: B

Question. The angle formed by the line of sight with the horizontal when the object viewd is below the horizontal level is
(a) corresponding angle
(b) angle of elevation
(c) angle of depression
(d) complete angle

Answer: A

Fill in the Blanks

DIRECTIONS : Complete the following statements with an appropriate word / term to be filled in the blank space(s).

Question. The ............... is the line drawn from the eye of an observer to the point in the object viewed by the observer.
Answer: line of sight

Question. The ............. of an object viewed, is the angle formed by the line of sight with the horizontal when it is above the horizontal level, i.e., the case when we raise our head to look at the object.
Answer: angle of elevation

Question. The ....................... of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when we lower our head to look at the object.
Answer: angle of depression

Question. The top of a building from a fixed point is observed at an angle of elevation 60° and the distance from the foot of the building to the point is 100 m. then the height of the building is..
Answer: 100√3 m

True / False

DIRECTIONS : Read the following statements and write your answer as true or false.
A straight highway leads to the foot of a tower of height 50 m.
From the top of the tower, the angles of depression of two cars standing on the highway are 30° and 60°. [ 3 = 1.73]
Now, based on the above information, mark the given statements as true or false.

Question. Distance between the cars is 57.67 m.
Answer: True

Question. First car is at a distance of 38.90 m from the tower.
Answer: False

Question. Second car is at a distance of 86.50 m. from the tower.
Answer: True

Question. Car at point C is at a distance of 200 m away from the top of the tower.
Answer: False

Please click on below link to download CBSE Class 10 Mathematics Statistics Worksheet Set A