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NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex

The NCERT Solutions for class 1 to class 12 has been written so as to help the understudies in all the degree of evaluations. We have given nitty gritty answers for all the inquiries keeping the stamping plan for each question. This thus, encourages you expert the test with bright evaluations.

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The questions given within NCERT solutions are very diversified and represent almost the entire chapter, so all children should read them very carefully. Student should do deep analysis of solutions for class 9 to 12 specially.

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One of the best methods for the indirect measurement of length or height involve trigonometric rations. Trigonometry is extensively used in geography, navigation, astronomy, etc.

The knowledge of trigonometry is used to construct maps, determine the position of different islands in relation to the longitudes and latitudes. Horizontal Ray: A ray parallel to the surface of the Earth emerging from the eye of an observer is called a horizontal ray. Line of Sight: The line of sight or ray of vision is the line drawn from the eye of an observer to the point in the object viewed by the observer.

Angle of Elevation: The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level.

Angle of Depression: The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level.

What is the angle of elevation of the sun? From the top of a 7 m high building, the angle of elevation of the top of a tower is 60 and the angel of depression of its foot is Find the height of the tower. Two points A and B are on the same side of a tower and in the same straight line with its base.

The angles of depression of these points from the top of the tower are 60 and 45 respectively. If the height of the tower is 15 m, then find the distance between these points.

Surveyors have used trigonometry for centuries. During the survey in , the highest mountain in the world was discovered. From a distance of over km, the peak was observed from six different stations. In , this peak was named after Sir George Everest, who had commissioned and first used the giant theodolites. The theodolites are now on display in the Museum of the Survey of India in Dehradun.

The mathematician does not study mathematics because it is useful. 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. Tan C. Not defined. Cosc C. Sec C.

Cot C. Now, you must have understood all the important topics and terms covered in each section of class 10 maths chapter 9. Perfect understanding of NCERT class 10 chapter 9 Introduction helps you to focus on some points such as the weightage of the chapter, important questions that can be asked in the examination, types of questions that can be appeared in your, etc.

This will help you to solve the exam more confidently and also ensures you that you can finish your exam within a time-duration. As, there is a proverb that says "Practice makes the men perfect". It tells us the importance of practicing continuously in any subject to learn anything. Continuous practice is a must to learn any of the subjects. Practicing class 10 maths Chapter 9 NCERT solutions designed by Vedantu experts will bring accuracy and confidence in you as they are designed according to the caliber of the students.

It helps you to increase the speed of solving your problems and also bring more accuracy in you. With practicing NCERT questions more and more, you will be aware of the types of questions that can be asked in the examination. This will help you to solve your exam paper more confidently. Practicing not merely enhances your conceptual understanding but also enhances your logical reasoning.

Most of the time the questions asked in the examination are repeated and solving the previous questions helps you to solve the questions speedily and accurately in the exam. The solutions are designed by the subject experts of Vedantu. Chapter-wise questions and solutions are easily accessible.

Special guidance for the students preparing for their board examinations. Exercise questions are easily accessible. The solutions are well-explained in the comprehensive method. NCERT Solution for class 10 plays an important role in shaping the future of the students as the grades which the students will score will shape the future of the student.

The NCERT solution prepared by the professionals of Vedantu is a one-stop solution for all your queries related to class 10 maths chapter 9. Detailed explanation and stepwise solutions for each question prepared by the experts will help you to understand the concept in a better way.

The NCERT solutions prepared by the experts of Vedantu provides excellent material for the student to practice and make the learning process more effective. Solutions are framed keeping in mind the age of the students. The content of the topic is pointed, brief, and straightforward. Complex questions are divided into small parts and well-explained to save the students from taking the unnecessary strain.

Every question is explained with the relevant image to understand the question precisely. The solutions are designed under the latest syllabus and CBSE guidelines. The aim to provide the solution is to help the students to solve each question given in the board exams in no time. Why are Some Applications of Trigonometry Important?

Class 10 Chapter 9 some application of trigonometry is an important topic to discuss as it tells how trigonometry is used to find the height and distance of different objects such as the height of the building, the distance between the Earth and Planet and Stars, the height of the highest mountain Mount Everest, etc.

To solve the questions based on some applications of trigonometry class 10, it is necessary to remember trigonometry formulas, trigonometric relations, and values of some trigonometric angles.

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