Worksheet: Some Application of Trigonometry

# Some Application of Trigonometry Class 10 Worksheet Maths

### Multiple Choice Questions

Q1: 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
Q2. 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

Q3: 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) Do not change
(d) None of the above

Q4: 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°
Q5: The angle of elevation of the top of a building 30 m high from the foot of another building in the same plane is 60°, and also the angle of elevation of the top of the second tower from the foot of the first tower is 30°, then the distance between the two buildings is:
(a) 10√3 m
(b) 15√3 m
(c) 12√3 m
(d) 36 m
Q6: 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

Q7: 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

Q8: 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 (in m) standing straight is:
(a) 15√3
(b) 10√3
(c) 12√3
(d) 20√3
Q9: 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

Q10: 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

### Solve the following Questions

Q1: Two poles of equal heights are standing opposite to each other on either side of the road which is 80m wide. From a point between them on the road the angles of elevation of the top of the poles are 60°and 30°.find the height of the poles and the distances of the point from the poles.

Q2: A tree standing on a horizontal plane leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively α and β .Prove that the height of the top from the ground is .

Q3: A man sitting at a height of 20m on a tall tree on a small island in the middle of the river observes two poles directly opposite to each other on the two banks of the river and in line with the foot of tree. If the angles depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60° and 30° respectively. Find the width of the river.

Q4: Consider right triangle ABC, right angled at B. If AC = 17 units and BC = 8 units determine all the trigonometric ratios of angle C.

Q5: If C and Z are acute angles and that cos C = cos Z prove that ∠C = ∠Z.

Q6: In triangle ABC, right angled at B if sin A = 1/2 . Find the value of
1. sin C cos A – cos C sin A
2. cos A cos C + sin A sin C

Q7: In triangle ABC right angled at B, AB = 12cm and ∠CAB = 60°. Determine the lengths of the other two sides.

Q8: If θ is an acute angle and find θ.

Q9: Find the value of x in each of the following.

(i) cosec 3x =
(ii) cos x = 2 sin 45° cos 45° – sin 30°

Q10: Given sin A = 12/37, find cos A and tan A.

The document Some Application of Trigonometry Class 10 Worksheet Maths is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on Some Application of Trigonometry Class 10 Worksheet Maths

 1. What are some practical applications of trigonometry?
Ans. Trigonometry is used in various fields such as engineering, architecture, physics, and navigation. It helps in calculating distances, heights, angles, and determining the size and shape of objects. For example, it is used in surveying land, designing buildings, analyzing the motion of objects, and predicting the paths of celestial bodies.
 2. How is trigonometry used in navigation?
Ans. Trigonometry plays a crucial role in navigation. It is used to determine the position, direction, and distance between two points on the Earth's surface. By using trigonometric functions such as sine, cosine, and tangent, sailors and pilots can calculate the angles and distances needed to navigate accurately. This helps them plot their course, avoid obstacles, and reach their destination safely.
 3. Can you give an example of how trigonometry is used in architecture?
Ans. Trigonometry is extensively used in architecture to ensure the stability and aesthetics of structures. Architects use trigonometric principles to calculate the angles of incline for staircases, slopes for roofs, and angles for window placements. They also use trigonometry to determine the height and dimensions of buildings, ensuring that they are structurally sound and visually appealing.
 4. How does trigonometry help in analyzing the motion of objects?
Ans. Trigonometry is used to analyze the motion of objects by calculating various parameters such as displacement, velocity, and acceleration. By using trigonometric functions, scientists and engineers can break down complex motion into simpler components, understand the relationships between angles and distances, and predict the future positions of objects. This is essential in fields like physics, robotics, and mechanics.
 5. Why is trigonometry important in engineering?
Ans. Trigonometry is vital in engineering as it helps engineers design and analyze structures, machines, and systems. Engineers use trigonometric principles to calculate forces and stresses in materials, determine optimal angles and dimensions for components, and solve complex geometric problems. Trigonometry also plays a significant role in electrical engineering, telecommunications, and signal processing.

## Mathematics (Maths) Class 10

120 videos|463 docs|105 tests

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