Answer
cos α = $\frac{3}{5}$, cos β = $\frac{4}{5}$
Work Step by Step
Step 1: By Pythagoras theorem
$6^{2}$ + $a^{2}$ = $10^{2}$
$a^{2}$ = 100 - 36
a = $\sqrt 64$ = 8
a = 8
Step 2:
cos α = $\frac{length of adjacent}{length of hypotenuse}$
cos α = $\frac{6}{10}$ = $\frac{3}{5}$
Similarly cos β = $\frac{length of adjacent}{length of hypotenuse}$
cos β = $\frac{a}{10}$ =$\frac{8}{10}$ = $\frac{4}{5}$
Therefore cos α = $\frac{3}{5}$, cos β = $\frac{4}{5}$
