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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. The following are the concepts covered in the 'height and distance' Some applications of trigonometry. To measure the height of big towers or big mountains. To determine the distance of the shore from the sea.
To find out the distance between two celestial bodies. This chapter has a weightage of 12 marks in class 10 Maths Cbse board exams. One question can be expected from this chapter. The questions will be allocated with 1 mark, 2 marks, 3 marks or 4 marks. Discussion about the sections, exercise, and type of questions given in the exercise. The exercise aims to test your knowledge and how deeply you understood each formula and concept of the topic. The numerical questions given in this chapter are based on some applications of trigonometry.
To make you understand the topic and related concept, solved numerical problems are also given. Stepwise solutions are given for each of the solved examples.
It will help you to understand which concept and formula will be used to solve the given questions accurately. This section gives an introduction to some applications of trigonometry.
It tells you how trigonometry is used by different scholars throughout the world and its uses in different fields. It also tells you the way trigonometry is used to find the height and distance of different objects without actually measuring them.
In this section, some important terms such as a line of sight, horizontal level, angle of elevation, and angle of depression are discussed. All these important terms are discussed along with the solved examples based on them which will clear your concepts thoroughly and also helps you to solve the questions given in the exercise.
This exercise includes a total of 16 questions. Question No. Given Information. To calculate. The angle of elevation and the length of the rope are given. We have to calculate the height of the tower.
The distance of the object and angle of elevation are given. We have to calculate the height of the tree. The angle of elevation and height of the two slides are given. We need to calculate the length of the slide. Height of the object and the distance of the object are given. The angle of depression and height of the observer from the ground are given. We have to calculate the distance between two objects.
The angle of elevation from the ground to the bottom of the tower and angle of elevation from the ground to the top of the tower are given. Length of the statue, angle of elevation to the top of the statue and angle of elevation to the top of the pedestal are given.
We have to calculate the height of the pedestal. The angle of elevation of the top of the building from the foot of the tower, Angle of elevation of the top of the tower from the foot of the building and height of the tower are given. We have to calculate the height of the building. Angles of elevations of the top of the two towers and distance between the two poles are given. Find the height of the pedestal. If the tower is 50 m high, find the height of the building.
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. Find the height of the poles and the distance of the point from the poles. A TV tower stands vertically on a bank of a canal. Find the height of the tower and the width of the CD and 20 m from pole AB.
Determine the height of the tower. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. Find the distance travelled by the balloon during the interval. A straight highway leads to the foot of a tower. Find the time taken by the car to reach the foot of the tower from this point. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary.
Prove that the height of the tower is 6 m. The height or length of an object or the distance between two distinct objects can be determined with the help of trigonometric ratios. The observer is looking at the top of the pole. The angle BAC, so formed by the line of sight with the horizontal, is called the angle of elevation of the top of the pole from the eye of an observer.
In the above figure, the line AC, is the line of sight as the observer is looking downwards from the top of the building at A towards the object at C. From the above figure, if we want to find the height CD of the pole without actually measuring it, we need the following information: i Distance ED of the observer from the pole.
Assuming that the above three conditions are known we can determine the height of the pole in the following way. By adding AE to BC, you will get the height of the pole.
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