Question

Is $\sin A$ = $\frac{3}{5}$ , find $\cos A$ and $\tan A.$

Answer 1

We have,
$sinA=\frac{Perpendicular}{Hypotenuse}=\frac{3}{5}$
So, we draw a triangle ABC, right angled at B such that
Perpendicular = BC = 3 units and, Hypotenuse = AC = 5 units.
By Pythagoras theorem, we have
$A{C}^2=A{B}^2+B{C}^2$
$\Rightarrow 5^2=A{B}^2+3^2$
$\Rightarrow A{B}^2=5^2-3^2$
$\Rightarrow A{B}^2=16$
$\Rightarrow AB=4$
When we consider the t-ratios of $\angle A$, we have
Base = AB = 4, Perpendicular = BC = 3, Hypotenuse = AC = 5
$\therefore cosA=\frac{Base}{Hypotenuse}=\frac{4}{5}andtanA=\frac{Perpendicular}{Base}=\frac{3}{4}$