Question

in a right ∆ABC if <A is acute and tan A=^3|4 find the remaining t-ratio of<A​

Answer 1

Answer:

We have,

cosecA=

Perpendicular

Hypotenuse

=

1

10

So, we draw a triangle ABC, right angled at B such that

Perpendicular =BC=1 unit and, Hypotenuse =AC=

10

units.

By Pythagoras theorem, we have

AC

2

=AB

2

+BC

2

⇒(

10

)

2

=AB

2

+1

2

⇒AB

2

=10−1=9

⇒AB=

9

=3

When we consider the trigonometric ratios of ∠ A , we have

Base =AB=3, Perpendicular =BC=1, and Hypotenuse =AC=

10

∴sinA=

Hypotenuse

Perpendicular

=

10

1

cosA=

Hypotenuse

Base

=

10

3

tanA=

Base

Perpendicular

=

3

1

secA=

Base

Hypotenuse

=

3

10

and, cotA=

Perpendicular

Base

=

1

3

=3