Question

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

Answer 1

Let ΔABC be a right-angled triangle, right-angled at point B.

Given that,

sin A = 3/4

`(BC)/(AC) = 3/4`

Let BC be 3k. Therefore, AC will be 4k, where k is a positive integer.

Applying Pythagoras theorem in ΔABC, we obtain

AC² = AB² + BC²

(4k)² = AB² + (3k)²

16k ² − 9k ² = AB²

7k ² = AB²

AB = sqrt7k

`cos A = ("Side adjacent to"angleA)/"Hypotenuse"`

=`(AB)/(AC) = sqrt(7k)/(4k) = sqrt7/4`

`tan A = ("Side adjacent to"angleA)/("Side adjacent to"angleA)`

`= (BC)/(AB) = (3k)/(sqrt7k) = 3/sqrt7`