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Unit Test: Some Applications of Trigonometry | Mathematics (Maths) Class 10 PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

  • Question numbers 1 to 5 carry 1 mark each.
  • Question numbers 6 to 8 carry 2 marks each.
  • Question numbers 9 to 11 carry 3 marks each.
  • Question number 12 & 13 carry 5 marks each.

Q1: _______________________ is drawn from the eye of an observer to the targeted object. (1 Mark)

(a) A parallel line
(b) Line of sight
(c) Elevation line
(d) Depression line

Q2: A slope is built against a wall which makes an angle 30° with the ground and the height of the wall is 2 meters. Find the length of the slope in meters. (1 Mark)

a) 2
b) 4
c) 1
d) 3

Q3: The shadow of a tower is equal to its height at 10-45 a.m. The sun’s altitude is (1 Mark)

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Q4: In given figure, the value of CE is (1 Mark)Unit Test: Some Applications of Trigonometry | Mathematics (Maths) Class 10

(a) 12 cm
(b) 6 cm
(c) 9 cm
(d) 6√3 cm 

Q5: When the length of shadow of a vertical pole is equal to √3 times of its height, the angle of elevation of the Sun’s altitude is __________________________. (1 Mark)

Q6: The ratio of the height of a tower and length of its shadow on the ground is √3 : 1 what is the angle of elevation of the sun? (2 Marks)

Q7: A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder. (2 Marks)

Q8: An observer 1.5 m tall is 28.5 m away from a tower of height 30 m. Find the angle of elevation of the top of tower from his eye. (2 Marks)

Q9: A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h. (3 Marks)

Q10: The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill. (3 Marks)

Q11: A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill. (3 Marks)

Q12: At the foot of a mountain the elevation of its summit is 45°, after ascending 1000 m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain. (5 Marks)

Q13: The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are 30° and 60° respectively. Find the difference between the heights of the building and the tower and the distance between them. (5 Marks)


You can find the solutions of this Unit Test here: Unit Test (Solutions): Some Applications of Trigonometry

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FAQs on Unit Test: Some Applications of Trigonometry - Mathematics (Maths) Class 10

1. What are some real-world applications of trigonometry?
Ans.Trigonometry is widely used in various fields. In architecture, it helps in designing buildings and structures. In engineering, it is essential for analyzing forces and designing mechanical systems. Navigation relies on trigonometric functions to determine positions and routes. Additionally, it plays a significant role in computer graphics, enabling the creation of realistic images and animations.
2. How is trigonometry used in astronomy?
Ans.In astronomy, trigonometry is used to calculate distances to stars and planets. By measuring angles and using the principles of triangulation, astronomers can determine the position of celestial bodies. This is essential for mapping the universe and understanding the motion of objects in space.
3. Can you explain how trigonometry is applied in construction?
Ans.Trigonometry is crucial in construction for determining structural integrity and ensuring proper angles and measurements. It helps in calculating heights, distances, and angles when laying out buildings, roofs, and other structures. Builders use trigonometric ratios to ensure that everything is level and aligned correctly.
4. What role does trigonometry play in navigation?
Ans.Trigonometry is vital in navigation, especially in maritime and aerial navigation. It is used to calculate distances between points and to determine the direction of travel using angles. Navigators apply trigonometric principles to chart courses, ensuring they reach their destinations accurately.
5. How does trigonometry relate to physics?
Ans.Trigonometry is fundamental in physics, particularly in the study of waves, oscillations, and forces. It helps describe motion, analyze vectors, and understand the behavior of physical systems. For example, in mechanics, trigonometry is used to resolve forces into components, making it easier to analyze the movement of objects.
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