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NCERT Solutions for Class 9 Maths, Free NCERT Solutions NCERT Solutions for Class 9 Maths Chapter 11 Constructions is provided here for the benefit of students of class 9. Geometry is a fundamental concept that is useful in many fields. Therefore, it is necessary to learn the concept and understand its applications. Chapter 2 Maths Class 10 is based on polynomials. The different types of equations and their components have been described in this NCERT Maths Class 10 Chapter 2. You can easily learn the new concepts and solve the exercise questions by using the NCERT Solutions Class 10 Maths Chapter 2 and complete this chapter. The NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry gives a detailed explanation of all the questions given in the NCERT textbook. NCERT Solutions help you to score high marks in 10th CBSE board exams as well as increase your confidence level as all the trigonometry related concepts are well-explained in a.
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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.

And when the cartesian plane is divided into four equal parts, called quadrants. You also learn the representation of a point on the Cartesian plane here. Linear Equations with x and y which further makes the two sides of an equation equal. In this chapter, you also learn about the example of a linear equation in two variables. According to the mathematician Euclid who has explained in his book on geometry which is known as Elements. And geometry is called Euclid geometry. He explained geometric shapes and figures such as euclidean geometry, its elements, axioms and five important postulates etc.

Construction of Pyramids by the Egyptians is the example of extensive use of geometrical techniques used by the people. Lines are defined as a straight and have negligible depth or width.

There are many types of lines: perpendicular lines, intersecting lines, transversal lines, etc. An angle is a figure where two rays emerge from a common point. A line segment is a part of a line which have two end-points. It is the shortest distance and has a fixed length. Two lines are said to be parallel when they do not meet at any point known as Parallel Lines. And when a line intersects two lines at distinct points known as Transversal Line.

If two sides and the included angle of one triangle are equal to the corresponding sides known as SAS Criteria for Congruency. And where two triangles are congruent if two angles and the included side of one triangle are equal known as ASA Criteria for Congruency.

Here you know all about Properties of Isosceles triangle. A quadrilateral is a shape which has four sides. Here you learn about different types of quadrilateral including square, rectangle, parallelogram properties etc. Opposite angles in a parallelogram are equal. Diagonals of a rhombus bisect each other at right angles. And also learn about The Mid-Point Theorem.

Summary: Introduction to Quadrilaterals, square, rectangle, parallelogram properties, Properties of diagonal of a parallelogram, important results related to parallelograms, The Mid-Point Theorem.

Where the opposite sides and opposite angles of a parallelogram are equal. The distance from the centre of the circle to the outer line is known as radius. And where Diameter is the line which divides the circle into two equal parts. The circles divide the plane into two regions such as interior and exterior regions which has area and perimeter. Here you also learn about how to draw bisector of the given angle, construction of a perpendicular. Here you take the guide with construction steps and clear diagram.

Summary: Introduction, Basic constructions, some constructions of triangles, Constructions Class with Examples. A triangle. You learn about Statistics, that means: the extraction of meaningful information from a given set of data is called Statistics. Statistics is used in many fields, such as business in the market.

And also used in daily life such as in the field of Engineering, Medicine, Weather forecasting, etc. It can range between 0 and 1, 0 probability means the event or experiment be an impossible and probability of 1 means a certain event. Here you learn all about Probability, its Experiment, Sum of Probabilities of Favourable and unfavourable events etc. Probability is used in many fields in our daily life.

It helps you and so important for better understanding and scoring good marks in 9 class exams. All solutions are well-reviewed before provided.

You can study anywhere and anytime. You can also share these PDF links to your classmates as well. These solutions are given in easy method, and it may clear your all doubts and concepts clear. So you can get more marks with these high-quality study materials. All solutions are designed by following extensive research on the Math subject.

So you will able to solve a wide range of problems at any difficulty level. If the students practice thoroughly and revise with all syllabus, then they can score even out of marks. To score highest, you should have clear all concept. So students are advised to know all CBSE Syllabus for Class 9 Maths right from the beginning of the academic year of , that can help them to prepare a study plan for the final exam.

And there are 15 chapters in 9th Maths subjects. The annual exam, theory covers a total of 80 marks and where internal assessment includes 20 marks. Class 9th Chapter-Wise Marks Weightage.

It is an effective and the best way to make students understand the subject and exclusively to perform well in the final exams. The following theorems may be asked to prove in exams, rest are for application and motivation: 1. If two lines intersect, vertically opposite angles are equal. The sum of the angles of a triangle is 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.

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