Chapter 9 Some Applications of Trigonometry Notes Class 10

Chapter 9 Some Applications of Trigonometry Notes Dowload

 Class 10 Chapter 9 Some Application of Trigonometry Notes 

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. in solving  problems related to heights and distances. 

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. Theodolite is based on the principles of trigonometry, which is used for measuring  angles with a rotating telescope. In 1856, 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. 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. [When the eye turns upwards above the horizontal line]. 

Line of sight: It is the line drawn from the eye of an observer to the object viewed. 

Angle of Depression 

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. 

[When the eye turns downwards below the horizontal line].

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. If a person at O looks at an object P  lying below the eye level, then, ∠HOP is the angle of depression of P as seen from O. 

Note : Angle of depression of P as seen from O = angle of elevation of O, as seen from P.

∴ ∠AOP = ∠OPH 

Height and Distance Formulas

Trigonometry Ratios Table 

Height and Distance Important Points 

• In solving problems observer is represented by a point if his height is not given.
• 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. then angle  of elevation increases and if the observer moves away from the object, the angle of elevation decreases. 
• 
• 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 that  observer is at higher altitude than object.