Real-Life Uses of Trigonometry in Class 10 Maths
Some applications of trigonometry class 10 notes chapter 9 are available with NCERT Solutions at Vedantu. The notes are typically designed by the mathematics masters at the top-notch online education portal keeping in mind the updated pattern and guidelines by the CBSE board. These quick notes on CBSE class 10 maths will help you to significantly refine your trigonometric skills as well get to the core of the topic in no time.
In addition, you can also check other Maths learning resources such as previous year question papers, sample papers, activity quizzes etc. all for free download at Vedantu.
Examples of Class 10 Chapter 9 - Some Applications of Trigonometry
Under this section, you will find the solved questions of chapter 9 – Some Applications of Trigonometry from Class 10 Maths textbook along with answer keys. These solutions are available for free PDF download from the given link at Vedantu official. Let’s get started with the solved Maths Class 10 chapter 9 questions.
Example: A villager is climbing a coconut tree using a 20 m long rope, which is tightly tied from the top of a vertical pole to the ground. Evaluate the height of the coconut tree, if the angle formed by the rope with the ground level is 30°. You can find the illustration below.
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Solution: Given that length of the rope named AC = 20m
Angle formed is ∠ACB = 30°
Let the height AB of the coconut tree be h (meters)
With that, in right ▲ABC,
sin 30° = AB/AC
½= h/20 (since sin 30° = ½)
H = 20/2 = 10metres
Therefore, the height of the coconut tree is 10m
Example: The facilities department of a housing society plans to put two slides for the kids to play in a park. For the kids below the age of 5 years, they want to have a slide whose top is at a height of 1.5 m, and is disposed at an angle of 30° to the ground, while for older children, they prefer to have a steep slide based at a height of 3 m, and inclined at an angle of 60° to the ground. Find out the length of the slide in both the cases?
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Solution:
Let the length of the slide for children below 5years of age x and the length of the slide for older children be y.
Given that: AF = 1.5 m and BC = 3m
∠FEA = 30°and ∠CDB = 60°
In right ▲FAE, sin 30°= AF/EF = 1.5/x
½ = 1.5/x
Thus x= 3m
In right ▲CBD, sin 60°= BC/CD = 3/y
√3/2 = 3/y
Thus, y = 3*2 / √3 = 2√3m
Therefore the length of the slide for children below 5years of age is 3m and the length of the slide for older children is 2√3m.
Example: An air balloon is flying above the ground at a height of 60 m. The string joined to the balloon is temporarily tied to a point on the ground. The inclination of the string with the ground level is 60°. What will be the length of the string, supposing that there is no slack in the string?
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Solution: Given that: AB = 60m and ∠ACB = 60°
Let AC be the length of the string
Then, in the right ▲ABC, sin 30°= AB/AC
= √3/2 = 60/AC
AC= 60*2/√3/ * √3/√3
= 120* √3 / 3
= 40√3
Therefore, the total length of the string is 40√3m
FAQs on Applications of Trigonometry for Class 10: Explained
1. What are the main concepts covered in the Class 10 chapter 'Applications of Trigonometry'?
This chapter primarily focuses on using trigonometry to solve real-world problems involving heights and distances. The key concepts you will learn include:
- Line of Sight: The imaginary line from an observer's eye to the object being viewed.
- Angle of Elevation: The angle formed by the line of sight and the horizontal when the object is above the horizontal level.
- Angle of Depression: The angle formed by the line of sight and the horizontal when the object is below the horizontal level.
2. What are some real-life examples where 'Applications of Trigonometry' are used?
Trigonometry has numerous real-world applications. Some common examples relevant to this chapter include:
- Architecture and Engineering: Calculating the height of buildings, towers, and bridges without direct measurement.
- Navigation: Used in aviation and shipping to determine locations and distances using angles.
- Astronomy: Measuring the distance to nearby stars and planets.
- Geography: Creating maps and determining the height of mountains or depths of oceans.
- Surveying: Used by surveyors to measure land areas and boundaries.
3. What is the difference between the angle of elevation and the angle of depression?
The primary difference lies in the observer's viewpoint relative to the object.
- The angle of elevation is formed when an observer has to look upward from a horizontal line to see an object. It is the angle between the horizontal line and the line of sight to the object above.
- The angle of depression is formed when an observer has to look downward from a horizontal line to see an object. It is the angle between the horizontal line and the line of sight to the object below.
4. Which key trigonometric ratios are essential for solving problems in 'Applications of Trigonometry'?
For Class 10, the three basic trigonometric ratios are essential for solving problems in this chapter. They are defined for a right-angled triangle:
- Sine (sin θ) = Length of the side Opposite to angle θ / Length of the Hypotenuse
- Cosine (cos θ) = Length of the side Adjacent to angle θ / Length of the Hypotenuse
- Tangent (tan θ) = Length of the side Opposite to angle θ / Length of the side Adjacent to angle θ
5. How do we decide whether to use sin, cos, or tan when solving a height and distance problem?
The decision depends entirely on which sides of the right-angled triangle are known and which side you need to find, relative to the given angle (θ). A simple way to remember is the mnemonic SOH-CAH-TOA:
- Use tan θ if your problem involves the Opposite and Adjacent sides. (TOA)
- Use sin θ if your problem involves the Opposite side and the Hypotenuse. (SOH)
- Use cos θ if your problem involves the Adjacent side and the Hypotenuse. (CAH)
6. How do architects or engineers use the concepts from 'Applications of Trigonometry' in their work?
Architects and engineers rely heavily on trigonometry for precision and safety. For instance, an architect might use the angle of elevation to determine the required height of a building based on the shadow it will cast at a certain time of day. Engineers use these concepts to calculate the slope of a ramp for accessibility, the span and height of bridge arches, and the forces acting on a structure. It is fundamental for ensuring that designs are not only aesthetically pleasing but also structurally sound and safe.
7. Why are the standard trigonometric values for angles like 30°, 45°, and 60° so important in this chapter?
According to the CBSE syllabus for Class 10, problems in 'Applications of Trigonometry' are typically based on these standard angles (30°, 45°, 60°). This is because these angles yield exact, rationalised values for sin, cos, and tan (e.g., sin 30° = 1/2, tan 45° = 1). Using these standard values allows students to solve problems manually without needing a calculator, focusing their efforts on understanding the problem setup and application of the correct ratio, rather than complex calculations. Memorising these values is crucial for solving board exam questions efficiently.
8. Is 'Applications of Trigonometry' a difficult chapter for Class 10 students?
The difficulty of this chapter is subjective, but many students find it manageable and high-scoring with consistent practice. The challenge often comes from visualising the problem and correctly drawing the right-angled triangle from the word problem. Once the diagram is correctly set up, the mathematical part involves applying a straightforward trigonometric ratio. Unlike other chapters with complex formulas, this one relies on a few core concepts, making it less about memorisation and more about logical application and visualisation.
