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NCERT Solutions for Class 9 Maths Chapter 10 Circles
In Chapter 10 Class 9 of NCERT, Circles, Theorems are extremely important, we have provided detailed explanation of thetheorems of circlesas well asNCERT Solutionsof all questions and myboat105 boatplans this chapter, we will learnThebasics- What is a circle, radius. Check CBSE Class 9 Chapter-wise MCQs to clear all the fundamental concepts and score high marks in the Maths exam. All the questions are provided with correct a. Students should practise these sample papers once they complete studying the whole syllabus of Maths.

Height and Distance : One of the main application of trigonometry is to find the distance between two or more than two places or to find the height of the object or the angle subtended by any object at a given point without actually measuring the distance or heights or angles.

Trigonometry is useful to astronomers, navigators, architects and surveyors etc. Angles of elevation or angles of depression of the objects are measured by an instrument called Theodolite.

Theodolite is based on the principles of trigonometry, which is used for measuring angles with a rotating telescope. In , Sir George Everest first used the giant theodolite, which is now on display in the Museum of the survey of India in Dehradun. Let P be the position of the object above the horizontal line OA and O be the eye of the observer, then angle AOP is called angle of elevation.

It is called the angle of elevation, because the observer has to elevate raise his line of sight from the horizontal OA to see the object P. Line of sight : It is the line drawn from the eye of an observer to the object viewed. Let P be the position of the object below the horizontal line OA and O be the eye of the observer, then angle AOP is called angle of depression. It is called the angle of depression because the observer has to depress lower his line of sight from the horizontal OA to see the object P.

Below the eye level: If the object lies below the horizontal plane of our eyes, then we have to move our head downwards to view it.

In doing so, our lines of sight moves downwards through an angle and the angle, which the line of sight now makes with the horizontal line, is called the angle of depression of the object from our eyes.

Example : Let OH be the horizontal line at the eye level. An observer 1. Determine the angle of elevation of the top of the tower from the eye of the observer. A ladder 15 m long makes an angle of 60 o with the wall.

Find the height of the point where the ladder touches the wall. What is the angle of elevation of the sun? In Fig. An observer, 1. Find the height of tower. Height and Distance The directions of the objects can be described by measuring: Angle of elevation Angle of depression Angles of elevation or angles of depression of the objects are measured by an instrument called Theodolite.

In , Sir George Everest first used the giant theodolite, which is now on display in the Museum of the survey of India in Dehradun Angle of Elevation Let P be the position of the object above the horizontal line OA and O be the eye of the observer, then angle AOP is called angle of elevation.

In solving problems object is represented by a line segment and some times by a point if height or length is not considered. For example, AB is tower and point C is observer. A line drawn parallel to earth surface is called horizontal line. The angle of elevation and depression are always acute angles. If the observer moves towards the objects like tower, building, cliff, etc. If the angle of elevation of sun decreases, then the length of shadow of an object increases and vice-versa.

If in problems, the angle of elevation of an object is given, then we conclude that the object is at higher altitude than observer. The angle of depression implies Ch 9 Maths Class 10 Examples 10th that observer is at higher altitude than object. Height and Distance Questions 1. RD Sharma Class 12 Solutions.

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