According to the question
sinA =
Method : 1( By Theorem )
sinA =
Let,
Height from angle A = 3 x
Hypotenuse of triangle = 5 x
By Pythagoras Theorem
Hypotenuse^2 = height^2 + base^2
( 5 x )^2 = ( 3 x )^2 + ( base )^2
25x^2 - 3x^2 = ( base )^2
16x^2 = base^2
( 4x )^2 = ( base )^2
4x = base
Therefore, cosA =
=
=
And, tanA =
=
=
Method : 2 ( Identities )
We know, sin^2 A + cos^2 A = 1
Substituting value,
( 3 / 5 )^2 + cos^2 A = 1
cos^2 A = 1 - 9 / 25
cos^2 A = ( 25 - 9 ) / 25
cos^2 A = 16 / 25
cos^2 A = ( 4 / 5 )^2
cos A = 4 / 5
tanA = sinA / cosA
= ( 3 / 5 ) / ( 4 / 5 )
=3/4