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This negative attitude towards their subject stops them from focusing on the math problems. They get nervous before exams even before a small class test as they are not at all prepared. To get rid from this situation, students need to hold a strong grip on this subject. If you hold it tightly, you can collect as many marks as you want.

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Trigonometric ratios of an acute angle in a right triangle express the relationship between the angle and the length of its sides. Note: The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle, if the angle remains same. An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle s involved.

Solution: Ex 8. Solution: Class 10 Maths Introduction To Trigonometry Trigonometry Trigonometry is the study of relationships between the sides and angles of a right-angled triangle.

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. About the Chapter. In the Class 10 Maths Chapter 9, you will study about different ways in which trigonometry is used to find the height and distance of different objects without actually measuring them. This chapter is divided into 3 sections and one exercise. The first section is the basic introduction of trigonometry in which you will learn, how the need for the trigonometry arose and its application in different fields.

The second section includes an introduction to height and distance, important terms related to the height and distance, conditions where the trigonometry concepts are used along with the examples, and last but not the least one exercise at the end. The questions asked in the exercise are based on the basic concepts of trigonometry and its application.

The third section includes a summary of the chapter where some important terms given in the chapter are discussed. Some Applications of Trigonometry. List of topics and exercise covered in Class 10 Chapter 9 Some applications of trigonometry. Section 9. Exercise 9. This exercise included 16 questions. In the ch 9 Maths class 10, we will be learning about trigonometry, some application of trigonometry, and the entire summary of the chapter.

What is Trigonometry? Trigonometry is one of the most historical subjects studied by different scholars throughout the world. As you have read in Chapter 8 that trigonometry was introduced because its requirement arose to astronomy. Since then trigonometry is used to calculate the distance from the Earth to the stars and the planets.

The most important use of trigonometry is to find out the height of the highest mountain in the world i. Mount Everest which is named after Sir George Everest.

It is also widely used in Geography and navigation. The knowledge of trigonometry enables us to construct maps, evaluate the position of an island concerning the longitudes and latitudes.

Historical Facts. Let us Turn to the History of Trigonometry. The trigonometry was used by surveyors for centuries. The highest mountain in the world was discovered during the survey in From a distance of over km, this peak was seen from 6 distinct stations.

This peak was named after Sir George Everest who had first used the theodolites. Theodolites are now exhibited in the museum of the surveys of Dehradun.

Surveying instrument, which is used for measuring angles with a rotating telescope. Height and Distance. In this topic, you will study about the line of sight, angle of elevation, horizontal level, and angle of depression.

All these terms are explained in a detailed form along with some solved examples based on it. These solved examples based on the terms line of sight, angle of elevation and angle of depression will help you to understand the concepts thoroughly. How to Calculate Height and Distance? Trigonometric ratios are used to find out the height and the distance of the object. For example: In figure 1, you can see a boy looking at the top of the lampost.

AB is considered as the horizontal level. This level is stated as the line parallel to the ground passing through the viewer's eyes. AC is considered as the line of sight. An inclinometer or Clinometer is a device usually used for measuring the angle of elevation and the angle of depression.

Let us recall some trigonometric ratios which help to solve the questions based on class 10 maths Chapter 9. Trigonometry Ratios. The ratio of the sides of a right-angle triangle in terms of any of its acute angle triangle is known as the trigonometric ratio of that specific angle. Sine - The sine of an angle is stated as the ratio of the opposite side perpendicular side to that angle to the hypotenuse side.

Cosine- The cosine of an angle is stated as the ratio of the adjacent side to that angle to the hypotenuse side. Tangent - The tan of an angle is stated as the ratio of the opposite side perpendicular side to that angle to the side adjacent to that angle. Cosecant- It is the reciprocal of sine.

Secant- It is the reciprocal of cosine. Cotangent- It is the reciprocal of tangent. The following trigonometry ratio table is used to calculate the questions based on applications of trigonometry class 10 NCERT solutions. Sin C. Cos C. It has four exercises covering problems related to trigonometric ratios, identities, and ratios of complementary angles.

Our solutions for Class 10 Maths Chapter 8 will help you to understand basic concepts in trigonometry. To practice and easily revise problems related to trigonometry ratios, trigonometric identities and ratio of complementary angles use solutions for Chapter 8 of Class 10 Maths.

This chapter includes only one exercise implementing the use of trigonometry in real-life situations. Learn and revise the applications of trigonometry and the questions based on them with our solutions for Chapter 9 for Class 10 Maths. In this chapter of Class 10 Maths, there are around 20 problems in two exercises based on circles and their properties.

The solutions for Class 10 Maths Chapter 10 provides a clear understanding of concepts such as tangent, tangent to a circle, number of tangents that can be drawn to circle and theorem based on them. It also helps in understanding the relevance of the radius, the diameter, and the properties and length of tangents drawn to a circle. There is only one exercise in chapter 11 of Class 10 Maths which has questions based on the constructions and the justification for the same.

The solutions for Class 10 Maths Chapter 11 will help you to learn the concept of drawing tangents to a circle along with accurately creating division of a line segment in a given ratio. Chapter 12 of Class 10 Maths textbook has 3 exercises and in this chapter, you will learn some concepts based on problems related to calculating the area and perimeter of circles, area of sectors and segment of a circle, area of some plane figures which are a combination of some shapes, etc.

Our solutions for Chapter 12 of Class 10 Maths will help you to easily grasp these concepts for a thorough revision. Our solutions of Grade 10 Maths Chapter 13 will help you to understand and learn the concept of area and volume of solids that we encounter in our day to day life such as cuboid, cube, sphere, and cylinder. In this chapter of Statistics, you will learn the concept of mean, median and mode of grouped data.

You will also understand the grouping and ungrouping of data. Our solutions for Chapter 14 will simply help you to revise cumulative frequency curves by implementing the learning and practice. In this chapter, you will learn how to find the possible outcomes of a random event occurring. The solutions for Class 10 Maths Chapter 15 will help you to learn and solve simple problems based on the concept of theoretical probability.

Related Sections. Frequently Asked Questions. NCERT Solutions for Class 10 students cover all the important topics and concepts required for a strong mathematical foundation. Exclusively designed by highly qualified educators of the country, these solutions serve as an all in one math learning guide for Class 10 students. Created by the best math experts in the country after long research and analysis, these solutions are exclusively designed to impart a strong conceptual knowledge in students through continuous practice.

These solutions serve as an excellent resource to prepare students for the Class 10 exam. They not only help students in preparing for exams but also builds their confidence to face various competitive exams with a positive approach. These solutions are well structured in a very simple and easy language to optimize self-learning in children.

With these solutions, students grasp concepts better in a shorter time limit thus learning time-management for exams. Providing coverage to all the important topics and concepts, these solutions are helpful in preparing for various competitive exams including Math Olympiad , NTSE, etc.

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