Question

If tan A = `4/3`, find sin A and cos A.

Answer 1

Given `tan A = 4/3`.

Let Perpendicular (P) = 4k and Base (B) = 3k.

Hypotenuse (H) = `sqrt((4k)^2 + (3k)^2`

= `sqrt(16k^2 + 9k^2)`

= `sqrt(25k^2)`

= 5k

Now, calculate sin A:

`sin A = P/H`

= `(4k)/(5k)`

= `4/5`

Calculate cos A:

`cos A = B/H`

= `(3k)/(5k)`

= `3/5`

`sin A = 4/5` and `cos A = 3/5`