Angle of Elevation and Depression | Trigonometry


Hello dear students, we are going to learn about angle of elevation and depression in this article. I will show you from basic to complex numerical problems related with elevation and depression. 

Angle of Elevation and Depression


This topic is taught in Mathematics textbook of class 9 and 10. If we observe somebody or something, sitting or standing from ground, our eyesight makes an angle with the ground taking we as a point on ground. That angle is known as angle of elevation. But if we observe something on the ground sitting on the top of buiding, our eyesight makes an angle with the horizon, that angle is known as angle of depression. Are you clear, right? If not, look the figure below and observe the fact.

Angle of Elevation

Angle of depression



I hope that above drawn figures clearly illustrate the meaning of angle of elevation and angle of depression. We have to do numerical problems on this topic to understand more clearly.

Numerical problems related to angle of elevation and depression.

Q.N.1) A boy sitting on the ground observe the height of the tree making eyesight an angle of 30 degree. If he is at a distance of 50m apart from the ground level of tree. Then, what will be the height of the tree?

= Solution.

Here, Let observe the figure below.



The boy is sitting so, it marked as a point in the diagram. He is 50 m apart from the tree and he makes an angle of  

Let's find the height of tree. In the above right angled triangle eyesight is hypotenuse (h), height of tree is perpendicular (p)  and distance of tree is base(b).

According to trigonometric ratios,

tan30=    

or     =  

or,p=
Hence, the required height of the tree is .m

Q.N.2)A boy sitting on the ground observing the tree of height   m and his distance from the tree is 50m. Now,find the angle made during observation of height of tree.

=Solution.

Here, Let observe the figure below.
Consider angle be A.

As we know, 
                        tanA=    

                        tanA=     

                         A= 30.

Hence,the required angle of elevation is 30 degree.




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