Question

If $\sin A=\frac{3}{4}$, then what is the value of $\cos A$?

• A. $\frac{4}{5}$
• B. $\frac{\sqrt{7}}{4}$
• C. $\frac{4}{3}$
• D. $\frac{5}{3}$

Answer 1

The correct option is B $\frac{\sqrt{7}}{4}$

Given,
$\sin A=\frac{3}{4}$
So, the perpendicular is 3 and the hypotenuse is 4.
Let's find the base.

$\begin{array}{cc}{4}^2& =3^2+{\text{Base}}^2\\ 16& =9+{\text{Base}}^2\\ {\text{Base}}^2& =16-9\\ & =7\\ \text{Base}& =\sqrt{7}\end{array}$

We know that, $\cos A=\frac{\text{Base}}{\text{Hypotenuse}}$

Thus,
$\cos A=\frac{\sqrt{7}}{4}$