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Some of the key trigonometric identities used in this chapter are as follows:. Consider right triangle ABC, right angled at B. Determine the lengths of the other two sides. What are the values of A, B, and C? Register in 2 easy steps and Start learning in 5 minutes! Phone: 91 44 Mobile: 91 GRE Online Courses. GRE Coaching in Chennai.
GRE Questions. GRE Preparation Videos. CAT Coaching Online. CAT Coaching in Chennai. 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. 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. According to the guidelines set by CBSE, all answers are written. The content, which is short and self-explanatory, and well organized. To enhance the understanding of the topic, some of the answers include relevant infographics and images.
During the revision of the test, it is useful and acts as a note. For you to solve the maximum questions and to get the chapter's command, solutions are kept simple. In chapter Linear Equations in two variables, these NCERT Solutions are written specifically so that students do not face any difficulties while solving any questions. In the form of solutions, it covers the whole syllabus and theory.
Chapter-wise solutions for different subjects are also available for the convenience of students. Download the Vedantu app right now and use the study material on the go. Given Information To calculate 1. 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 3. The angle of elevation and height of the two slides are given We need to calculate the length of the slide 4. The distance of the object and angle of elevation are given We have to calculate the height of the tower. Height of the object and the distance of the object are given We have to calculate the height of the tower.
The angle of depression and height of the observer from the ground are given We have to calculate the distance between two objects 7. 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 We have to calculate the height of the tower.
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 9.
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