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

16k² − 9k² = AB²

7k² = AB²

AB = `sqrt7k`

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

∴ cos A = `("AB")/("AC")`

= `sqrt(7k)/(4k)`

= `sqrt7/4`

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

= `("BC")/("AB")`

= `(3k)/(sqrt7k)`

= `3/sqrt7`