Introduction to Trigonometry Applications
In Class 10 Maths Chapter 9, we explore the real-world applications of trigonometry. This chapter focuses on solving problems related to heights and distances using trigonometric ratios. These concepts are widely used in fields like engineering, architecture, navigation, and physics.
Topics Covered in Chapter 9: Some Applications of Trigonometry
- Introduction – Basic understanding of trigonometric concepts.
- Heights and Distances – Applications of trigonometry to measure heights of objects and distances between points using angles of elevation and depression.
- Summary – Key points and formulas covered in the chapter.
NCERT Solutions for Class 10 Maths Chapter 9 – All Exercises
This post provides NCERT solutions for all exercises of Chapter 9 – Some Applications of Trigonometry. These solutions are useful for board exam preparation, homework, and revision.
Example Problem from Chapter 9
Problem: A circus artist is climbing a 20-meter-long rope that is tightly stretched and tied from the top of a vertical pole to the ground. If the rope makes an angle of 30° with the ground, find the height of the pole.
Solution:
We use the sine formula: sin(θ)=oppositehypotenuse\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
Given:
- Angle θ=30∘\theta = 30^\circ
- Rope length (hypotenuse) = 20 m
- Height of the pole (opposite side) = ?
sin(30∘)=Height of Pole20\sin(30^\circ) = \frac{\text{Height of Pole}}{20}
Since sin(30∘)=12\sin(30^\circ) = \frac{1}{2}, 12=Height of Pole20\frac{1}{2} = \frac{\text{Height of Pole}}{20} Height of Pole=20×12=10m\text{Height of Pole} = 20 \times \frac{1}{2} = 10 m
Final Answer: The height of the pole is 10 meters.
NCERT Solutions for Class 10 Maths
CBSE NCERT Solutions for Class 10 Maths in PDF form to free download or use online for Gujarat Board, UP Board, MP Board, CBSE, KSEEB, Kerala and other board following NCERT books.
- Chapter 1 Real Numbers
- Chapter 2 Polynomials
- Chapter 3 Pair of Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 5 Arithmetic Progressions
- Chapter 6 Triangles
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 9 Some Applications of Trigonometry
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability
Why Trigonometry is Important
- Helps in construction and engineering.
- Used in navigation to find distances.
- Essential in physics for measuring angles and heights.
Conclusion
Class 10 Maths Chapter 9, “Some Applications of Trigonometry”, is an important chapter that helps students understand practical uses of trigonometry. These NCERT solutions provide a step-by-step approach to solving problems efficiently.
Keywords for SEO: NCERT Solutions, Class 10 Maths, Chapter 9, Some Applications of Trigonometry, Trigonometric ratios, Heights and distances, Angle of elevation, CBSE Maths solutions, Class 10 Maths PDF solutions.