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Angles of Elevation and Depression

One of the most important applications of trigonometry is in the determination of heights and distances of distant objects that are not directly measurable, by observations of angles subtended by those objects at the eye of the observer.

Trigonometry plays a very important part in land survey. It is also extensively used by astronomers in determining the distance of the heavenly bodies like the sun, moon and stars.

Two types of angles are very often used in the practical applications of trigonometry and they are obtained as follows.

Angle of Elevation
 


The angle above the horizontal that an observer must look to see an object that is higher than the observer is called ‘Angle of Elevation’.                              


Angle of Depression
The angle below the horizontal that an observer must look to see an object that is lower than the observer is called ‘Angle of Depression’.      
       

In the diagram

CAB is the angle of elevation and ACD is the angle of depression.
The direction of the arrow is from A to C for angle of elevation and the direction of the arrow from C to A for the angle of depression.

These two angles and the trigonometric ratios are used to determine the heights and distances of distant objects.

 




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