In this presentation the main focus is on understanding the relationships between three sides and three angles of a triangle using some basic ratios called trigonometric ratios. We also discussed Pythagoras theorem to determine the value of hypotenuse or base or perpendicular in a right angled triangle using its standard formulae. We discussed about how to determine the perpendicular and base with respective to a specific angle in right angled triangle. We can apply these trigonometric ratios and Pythagoras theorem concepts in solving questions of class 10th NCERT, RBSE or any other board books. ................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .......................VIDEO LECTURE OF THIS PRESENTATION.................................. .................................... https://youtu.be/iPaiMb1OvN0 ......................................... .............................. https://mathsolutionpoint.blogspot.com/p/10-th.html ...................

1. Trigonometric Ratios
&
Pythagoras Theorem
Fundamental Concepts
Class-X (NCERT, RBSE)

2. Trigonometry Ratios
Consider a right triangle ABC as shown in adjacent figure :
1. There are three angles in this triangle as follows :
A. AngleABC = 90 degree
B. Angle BAC = Acute Angle (less than 90 degree)
C. Angle BCA = Acute Angle(less than 90 degree)
A
CB
Perpendicular
Base

3. Trigonometry Ratios
 If we consider angle BAC then :
1. Side opposite to this angle is called perpendicular
i.e. BC is perpendicular.
2. Side AC is called hypotenuse. And
3. Side AB is called Base. C
AB
Perpendicular
Base
A
CB
Perpendicular
Base
 Consider a right triangle ABC as shown in adjacent figure :
 If we consider angle BCA then :
1. Side opposite to this angle is called perpendicular i.e. is
AB perpendicular.
2. Side AC is called hypotenuse. And
3. Side BC is called Base.

4. Trigonometry Ratios
The trigonometry ratios with respect to angle BAC or angle A are as follows:
Ratio Formula Triangle ABC
sin A Perpendicular/Hypotenuse BC/AC
cosec A Hypotenuse/Perpendicular AC/BC
cos A Base/Hypotenuse AB/AC
sec A Hypotenuse/Base AC/AB
tan A Perpendicular/Base BC/AB
cot A Base/Perpendicular AB/BC
C
AB
Perpendicular
Base

5. Trigonometry Ratios
The trigonometry ratios with respect to angle BCA or angle C are as follows:
Ratio Formula Triangle ABC
sin C Perpendicular/Hypotenuse AB/AC
cosec C Hypotenuse/Perpendicular AC/AB
cos C Base/Hypotenuse BC/AC
sec C Hypotenuse/Base AC/BC
tan C Perpendicular/Base AB/BC
cot C Base/Perpendicular BC/AB
A
CB
Perpendicular
Base

6. Trigonometry Ratios
Additional ratios
With respect to angle A or angle BAC
sin A = 1/cosec A cosec A= 1 / sin A
cos A = 1 / sec A sec A = 1 / cos A
tan A = 1 / cot A cot A = 1 / tan A
Additional ratios
With respect to angle C or angle BCA
sin C = 1/cosec C cosec C= 1 / sin C
cos C = 1 / sec C sec C = 1 / cos C
tan C = 1 / cot C cot C = 1 / tan C

7. Pythagoras Theorem
(Hypotenuse)2 = (Perpendicular)2+(Base)2
(Perpendicular)2 = (Hypotenuse)2 - (Base)2
(Base)2 = (Hypotenuse)2 - (Perpendicular)2
A
CB
Perpendicular
Base
Pythagoras Theorem