Question

if cosA = 4/5 the value of sinA is​

Answer 1

Answer: sin A = ⅗

Explanation:

We know, cos^2 A + sin^2 A = 1

⇒ (4/5)^2 + sin^2 A = 1

⇒ sin^2 A = 1 - 16/25

⇒ sin A = √(9/25)

⇒ sin A = ⅗.

ALITER:-

In △ABC, cos A = AB/AC = 4/5.

Now, assume that AB = 4k and AC = 5k. So, by Pythagoras theorem,

BC = √(AC^2 - AB^2) = √(25k^2 - 16k^2) = 3k.

So, sin A = (Opposite side of ∠A)/(Hypotenuse) = BC/AC = 3k/5k = ⅗.