Question

Given that sinA = 2/3 and A is acute find cos(A)%7D%7B3%7D%20" id="TexFormula1" title=" \sin(a) = \frac{2}{3} " alt=" \sin(a) = \frac{2}{3} " align="absmiddle" class="latex-formula">

Answer 1

Recall that

$\sin^2a+\cos^2a=1\implies\cos^2a=1-\dfrac49=\dfrac59$

$\implies\cos a=\pm\dfrac{\sqrt5}3$

Angle $a$ is acute, which means its measure is between 0 and 90 degrees. For $0^\circ$, we have $\cos a>0$, so we should take the positive root. Then

$\cos a=\dfrac{\sqrt5}3$