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To solve any question on heights and distances, the first and foremost thing is to draw a clean, neat, and friendly diagram labelling all the available angles and sides.
The point of observation or measurement should also be included as a point in the triangle representing the question. Right angle or 90 degree is necessary to apply trigonometric ratios in such problems. The height, base, and hypotenuse should also be appropriately marked in the diagram to simplify it.
Line of Sight. Line of sight is a critical concept in trigonometry as it is based on the line of sight that angle of elevation and angle of depression is measured. When we look upon an object, an imaginary straight line connects our eyes, and the object is called the line of sight.
The angle of elevation is the angle made between the horizontal and our line of vision when we look up, and angle of depression is the angle between horizontal and the line of vision when we look down upon an object.
Besides the right angle or degree angle, the angle of elevation and angle of depression plays a significant role in measuring the height of buildings or the height of any such things from an observer's point of view. Based on these angles, trigonometric ratios Vedantu Class 10 Maths Ch 5 Uav are applied, and the base and height are decided.
If we look upon a building whose height is to be measured, the angle made is the angle of elevation, and if we are looking down for something whose depth is to be measured, the angle made is the angle of depression.
The unknown values which represent the height or distance to be measured are calculated in such a way by applying equations of trigonometric ratios to both known and unknown values. From it, the unknown is calculated. We must always take care that the unknown value should represent any one of the equation variables and apply trigonometric ratio, which includes that side. The unknown value may be based on, height or hypotenuse of the triangle.
Practising Important Questions of Class 10 Maths Chapter 9- Applications of trigonometry are the ultimate method to tackle any kind of questions from the topic. As we say Practice makes a man perfect, the same is the case for trigonometry too.
Once the basics are clear, students should go on solving NCERT questions and other important questions as well. Our expert team at Vedantu is delighted to provide students with the topic's best questions.
We make sure that questions are covered from every important topic so that students will not miss any of them. Practising important questions by Vedantu will provide in-depth knowledge about the topic, and at the same time make all the basic concepts very clear.
For every student who wishes to pass board exams with flying colours, it is a necessity to solve all the important questions by Vedantu so that your maths paper can turn easily. 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 Vedantu Class 10 Maths Ch 7 Universal 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.
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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. We have to calculate the height of the tower and the distance of the point from the poles. One angle of elevation from the bank of the river and another angle of elevation 20m away from the bank of the river are given. To calculate: Height of the tower, width of the canal. The angle of elevation, angle of depression and the length of the top of the building are given.
The angle of depression of two ships and the height of lighthouse from the sea level is given. We have to calculate the distance between two ships. The angle of elevation from one point to the top of the tower and angle of elevation from another point to the top of the tower are given.
We have to calculate the height of the tower and width of the canal. We have to calculate the time taken by the car to reach the foot of the tower. Angles of elevation from one point and angle of elevation from another point are complementary and also the distance between two points from where the angle of elevation is formed is 4 m and 9 m.
To prove: Height of the tower 6 m. The summary at the end of the chapter details a brief explanation of all the topics you covered in this chapter. Important Terms to Remember in Height and Distance. Line of Sight - It is a line that is drawn from the eye of an observer to the point on the object viewed by the observer. The Angle of Elevation - It is defined as an angle that is formed between the horizontal line and line of sight.
If the line of sight lies upward from the horizontal line, then the angle formed will be termed as an angle of elevation. Let us take another situation when a boy is standing on the ground and he is looking at the object from the top of the building. The line joining the eye of the man with the top of the building is known as the line of sight and the angle drawn by the line of sight with the horizontal line is known as angle of elevation. This angle is known as the angle of elevation.
The Angle of Depression - It is defined as an angle drawn between the horizontal line and line of sight. If the line of sight lies downward from the horizontal line, then the angle formed will be termed as an angle of depression. Let us take a situation when a boy is standing at some height concerning the object he is looking at. In this case, the line joining the eye of the man with the bottom of the building is known as the line of sight and the angle drawn by the line of sight with the horizontal line is known as angle of depression.
Note: Angle of elevation is always equal to the angle of depression. The important Point to Remember. The distance of the object is also considered as the base of the right angle triangle drawn through the height of the object and the line of sight.
The length of the horizontal level is also known as the distance of the object it forms the base of the triangle. Line of sight is considered as a hypotenuse of the right-angle triangle. Hypotenuse side is calculated using Pythagorean Theorem if the height and distance of the object are given.
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