Value Based Questions: Some Applications of Trigonometry

# Class 10 Maths Chapter 9 Question Answers - Some Applications of Trigonometry

Q1. A fire at a building B is reported on telephone to two fire stations F1 and F2, 10 km apart from each other on a straight road.

F1 observes that the fire is at an angle of 60° to the road and F2 observes that it is at angle of 45° from it. The station F1 sends its team.

(a) Why the team of station F1 was sent?
(b) How much distance the station F1 team will have to travel?
(c) Which mathematical concept is involved in the above problem?
(d) By sending its team, which value is depicted by the fire-station F1?

Sol. Let BL be the perpendicular from B on F1F2.

(a) ∵ BL ⊥ F1F2
and ∠ LF1B = 60°;
∠ LF2B = 45°
â From right-angled ΔF1LB and ΔF2LB, we have:

⇒

∴ sinθ increases as θ increases from 0° to 90°.
∴ sin 45° < sin 60°
⇒

∴ Distance of B from F2 is more than that of from F1. That is why the station F1 sent its team to B.

Let F1B be x km
⇒x cos 60° = F1L    ..........(1)

⇒ BL = BF1 sin 60°
⇒ F2L = x sin 60°    ..........(2)

........(3)

From (2) and (3), we get
F1L + F2L = 10

x cos 60° + x sin 60° = 10

⇒ x [cos 60° + sin 60°] = 10

∵ Station F1 team travelled 7.32 km
(c) Trigonometry [Heights and Distances]
(d) Promptness.

Q2. The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°. If the height of the tower is 40m, find the height of the chimney. According to pollution control norms, the minimum height of a smoke emitting chimney should be 100m. State if the height of the above mentioned chimney  meets the pollution norms.
What value is discussed in this question?

Sol. In the figure, the height of the tower (AB) = 40 m
Let the height of the chimney (CD) = h metre.

Thus, the height of the chimney is 120 m.
As, the minimum height of a chimney (according to the pollution control norms) should be 100 m
∴ 120 m > 100 m
∴ Thus, the above mentioned chimney meets the pollution norms.
Value : To keep pollution free environment.

The document Class 10 Maths Chapter 9 Question Answers - Some Applications of Trigonometry 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 Class 10 Maths Chapter 9 Question Answers - Some Applications of Trigonometry

 1. What are some real-life applications of trigonometry?
Ans. Trigonometry has numerous applications in various fields. Some examples include: - Architecture: Trigonometry helps architects in designing structures and calculating angles for stability and aesthetics. - Engineering: Trigonometry is used in various engineering disciplines such as civil, mechanical, and electrical for solving problems related to forces, vibrations, and circuit analysis. - Navigation: Trigonometry is crucial in navigation systems used by ships and aircraft. It helps determine positions, distances, and angles. - Astronomy: Trigonometry plays a significant role in understanding celestial bodies, calculating distances between stars, and determining their positions. - Physics: Trigonometry is applied in physics to analyze and solve problems related to waves, vibrations, and rotations.
 2. How is trigonometry used in measuring heights and distances?
Ans. Trigonometry is used to measure heights and distances when direct measurement is not feasible. One common method is the use of trigonometric ratios such as sine, cosine, and tangent. By measuring an angle and the length of one side, we can calculate the length of an unknown side using these ratios. For example, using a clinometer to measure the angle of elevation from the ground to the top of a tree, and knowing the distance from the tree, we can calculate the height of the tree using trigonometry.
 3. Can you give an example of how trigonometry is used in construction?
Ans. Trigonometry is extensively used in construction projects. One example is calculating the height of a building or a structure. By using a theodolite or a total station, an engineer can measure the angle of elevation from the ground to the top of the building. With this angle and the distance from the building, trigonometry can be applied to calculate the height of the building using the tangent function.
 4. How does trigonometry help in analyzing sound and light waves?
Ans. Trigonometry is used in analyzing sound and light waves by studying their periodic nature. By representing these waves as functions of angles, trigonometric functions like sine and cosine can be used to model and analyze their behavior. Trigonometry helps in understanding properties such as frequency, amplitude, phase, and wavelength of sound and light waves.
 5. In which sports is trigonometry used?
Ans. Trigonometry finds applications in various sports, especially those involving projectile motion or angles. Some sports where trigonometry is used include: - Archery: Trigonometry is used to calculate the optimal angle and force required to hit a target accurately. - Golf: Trigonometry helps golfers calculate the distance to the hole and determine the required angle and force to make shots. - Soccer: Trigonometry is used by players to calculate the angle and force required to score goals or pass the ball accurately. - Baseball: Trigonometry is used by pitchers to calculate the optimal angle and force needed to throw accurate pitches. - Shooting: Trigonometry is used in shooting sports such as rifle shooting and skeet shooting to calculate angles and trajectories for hitting targets accurately.

## Mathematics (Maths) Class 10

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