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2 votes
If sine
= 3/5 then tane =

User Lllllll
by
6.1k points

1 Answer

4 votes

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

User Pistal
by
6.6k points
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