Question

Given $tan A = \frac{4}{3} find \hspace{2} sin A \hspace{2} and \hspace{2} cosA$

Answer 1

Answer:

sinA = 4/5

cosA = 3/5

Step-by-step explanation:

Hi,

Given that tanA = 4/3

Construct  a right angled triangle ABC, right angled at B such that

BC = 4 units

AB = 3 units,

But, from pythogarus theorem, we know that AB² + BC² = AC²,

so AC² = 3² + 4² = 25 = 5²

Hence, AC = 5 units

tan A  = Opposite Side/ Adjacent Side = 4/3

Now, sin A is defined as Opposite Side/Hypotenuse

sinA = BC/AC = 4/5

Thus, sinA = 4/5.

Now, cos A is defined as Adjacent Side/Hypotenuse

cosA = AB/AC = 3/5.

Thus, cosA = 3/5.

Hope, it helps !