Trigonometry//Chapter 11.1//Question 5//SSC//10 th class maths

TRIGONOMETRY
SSC
Question.5
Chapter.11.1

Question 5.
If 3 tan A = 4, then find sin A and cos A. (AS1)
Solution:
Given that, 3 tan A = 4

Opposite side to ∠A = BC = 4k
Adjacent side to ∠A = AB = 3k
Now we have in ∆ABC, ∠B = 90°
∴ AC2 = AB2 + BC2 (By Pythagoras theorem)
= (3k)2 + (4k)2
= 9k2 + 16k2
= 25k2
∴ AC = 25k2−−−−√ = 5k
AC = 5k = Hypotenuse
sin A =  Opposite side  Hypotenuse 
= 4k5k = 45
cos A =  Adjacent side  Hypotenuse 
= 3k5k = 45

Trigonometric ratios are fundamental relationships between the angles and sides of a right triangle. They are used extensively in geometry, physics, engineering, and various fields of mathematics. The primary trigonometric ratios are based on a right triangle and are defined as follows:

Sine (sin):

Definition: The ratio of the length of the opposite side to the length of the hypotenuse.
Formula: [ \sin(\theta) = \frac{{\text{Opposite}}}{{\text{Hypotenuse}}} ] up

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