Answer
cos α = $\frac{5}{3sqrt5}$, cos β = $\frac{2}{3}$
Work Step by Step
Step 1: By Pythagoras theorem
$(sqrt of 5)^{2}$ + $a^{2}$ = $3^{2}$
$a^{2}$ = 9 - 5
a = $\sqrt 4$ = 2
a = 2
Step 2:
cos α = $\frac{length of adjacent}{length of hypotenuse}$
cos α = $\frac{sqrt 5}{3}$ * $\frac{sqrt 5}{sqrt 5}$ = $\frac{5}{3sqrt5}$
Similarly cos β = $\frac{length of adjacent}{length of hypotenuse}$
cos β = $\frac{2}{3}$
Therefore cos α = $\frac{5}{3sqrt5}$, cos β = $\frac{2}{3}$
