NCERT Notes for Class 10 Maths Chapter 9 Some Applications of Trigonometry
![NCERT Notes for Class 10 Maths Chapter 9 Some Applications of Trigonometry NCERT Notes for Class 10 Maths Chapter 9 Some Applications of Trigonometry](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQP-GfceJuYTzSLGquCnjLIOJFNFOYN1F-6H42Q6zmZxnxa8ijmpaqtweDej_SZlPfi-HK0zUqGytfjkOO9awJoHJDQmkB290EdTsJBdyPUffGfh_x4N2i9k_NPaKmeddpLNRNh6lYnJcdkVaZA1yNdtqOM0-UNw48FFOM-Jx8D9MZNvLJ2ESC9tvpSCQB/s16000/chapter9-some-applications-of-trigonometry-revision-notes-class10-maths.jpg)
Class 10 Maths Chapter 9 Some Applications of Trigonometry Notes
Chapter Name | Some Applications of Trigonometry Notes |
Class | CBSE Class 10 |
Textbook Name | NCERT Mathematics Class 10 |
Related Readings |
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Line of Sight
When an observer looks from a point E (eye) at object O then the straight line EO between eye E and object O is called the line of sight.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0s3f9lfq3i2lan2stlt5ElIv_ms3x8QvuCxcfHanpotGDRQJ4jGBYSLkswVTDGvK7Nm8e32AQHxJGpuSR68lmzkpGeRJdTU-0LDDBbwF6220My_UcEc-T1ackhGCzskauNAydHGN7NVPPGB-Yu0Rqa3msdwVx7sQLjXQr4607PU3tGV73jACvOHbzo-k/w192-h90/ncert%20class%2010%20chapter%209%20Some%20Applications%20of%20Trigonometry%20img%201.png)
Horizontal
When an observer looks from a point E (eye) to another point Q which is horizontal to E, then the straight line, EQ between E and Q is called the horizontal line.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikKrzkx7R02sEjXOWuqXr09qL0uztV2iA-EF3zOC1xRZCKktXVxnUm4HGCXheRj5y15dESw5otkeFkOzjaYWbaN-wZSv24r2doLsFh2x0xwe2YLFGpr_qq74S2VZ0DamY2HAsw8-YmXBGUs1ySBCaSNgVuGuin1mb30Xld7BFWDy_Cen39VmHebILSl-c/w209-h46/ncert%20class%2010%20chapter%209%20Some%20Applications%20of%20Trigonometry%20img%202.png)
Angle of Elevation
When the eye is below the object, then the observer has to look up from point E to object O. The measure of this rotation (angle θ) from the horizontal line is called the angle of elevation.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbIZZaLSKEOhVwag8ce3AR-2iu2miDtxwCIUVdJeU2z-CIHhqZ1s2rjhyb0_jI44LR77oNY7C6XC0DoZ_tH4aZhG3nfnVRm1yRX3txhwKKi7vT5l6wKqB0NmtL1Qd9BYhXEP7ZYYL-SmUkJrbX16TxxF-K0fh9RkXco4KNrt3W9PniHoHFIp51Z6SF_3c/w268-h139/ncert%20class%2010%20chapter%209%20Some%20Applications%20of%20Trigonometry%20img%203.png)
Angle of Depression
When the eye is above the object, then the observer has to look down from point E to the object. The horizontal line is now parallel to the ground. The measure of this rotation (angle θ) from the horizontal line is called the angle of depression.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-7XGjbuds6gZ4AgczsJ2WzlPm8nLF42nSXzap3hq3eGOd6sHaLi0_UUnYeewNjrGcdAIJWPaV0mfilNMGbEVV6PozNaYIMovlhat3VMtzGOP_2vu1dfPXP-dGL7-GwU-uxHa-5Md6csTF7ud-bGQT-UlZkIp3-6TicPdiFmYxelQwxausxpkFaIoXUeM/w242-h133/ncert%20class%2010%20chapter%209%20Some%20Applications%20of%20Trigonometry%20img%204.png)
How to convert the above figure into the right triangle
Case I: Angle of Elevation is known
Draw OX perpendicular to EQ.
Now ∠OXE = 90°
ΔOXE is a rt. Δ, where
OE = hypotenuse
OX = opposite side (Perpendicular)
EX = adjacent side (Base)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbfXqIOTBgvxnkyji5m219qrL_4DPJzsZ3nPmSjlNQ-mCXWY9Xmuz4u7WToXRb9th2HXORh5IZs-RK3bDhHKOqahdPyE0lH_xqs9-MpI97Pht5b-fy90EF87nKkYgB37svpKOCi9c6Pp7kwp5igVKazAHwooUEUy1Qy48zOwb5Q_hdXfeotbEXZRPabRg/w233-h156/ncert%20class%2010%20chapter%209%20Some%20Applications%20of%20Trigonometry%20img%205.png)
Case II: Angle of Depression is known
(i) Draw OQ’parallel to EQ
(ii) Draw perpendicular EX on OQ’.
(iii) Now ∠QEO = ∠EOX = Interior alternate angles
ΔEXO is an rt. Δ. where
EO = hypotenuse
OX = adjacent side (base)
EX = opposite side (Perpendicular)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyMgncf5xU8vSonePg4ZLRbY8SnI6YqvJhXVCMa-J99JTzK67jtKVNi51OoG7YdZZJMicms-3jZwBoHb5HmfOIVszVw8m0hJ-arO5TXUQ6eASqL8M5SGkaIZ6X3dQVNC7rXIMF6A1JrEfpUXXyUaXOaQA8uqGjmVgJhPCVEFe7MsTya8QR_HBNRuL8F3Q/w238-h163/ncert%20class%2010%20chapter%209%20Some%20Applications%20of%20Trigonometry%20img%206.png)
- Choose a trigonometric ratio in such a way that it considers the known side and the side that you wish to calculate.
- The eye is always considered at ground level unless the problem specifically gives the height of the observer.
The object is always considered a point.
Some People Have
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg57Sd6M0ur21Q1ecT0UQXrboIAElN0ZEPqjBde_hGiVY2fP8fggtzCRd9aP8hBlnm9EWDZXU7XRh7K5xJYk6FV1HwDcE15ttySkZKoVKzis_iV-cW3inifehEeGk9-wAUR408qGkFFdg7Qzmy6nQpEw9nkuL7WirjzWHrJHI7JypPobVE1ZIc3Bsw4N_I/w208-h168/ncert%20class%2010%20chapter%209%20Some%20Applications%20of%20Trigonometry%20img%207.png)