Recall that
[tex]\sin^2a+\cos^2a=1\implies\cos^2a=1-\dfrac49=\dfrac59[/tex]
[tex]\implies\cos a=\pm\dfrac{\sqrt5}3[/tex]
Angle [tex]a[/tex] is acute, which means its measure is between 0 and 90 degrees. For [tex]0^\circ<a^\circ<90^\circ[/tex], we have [tex]\cos a>0[/tex], so we should take the positive root. Then
[tex]\cos a=\dfrac{\sqrt5}3[/tex]
