In the given triangle by using Pythagoras theorem ,
[tex]\begin{gathered} 17^2=x^2+8^2 \\ x^2=17^2-8^2 \\ x^2=\text{ 289 - 64} \end{gathered}[/tex]
Further,
[tex]\begin{gathered} x^2\text{ = 225} \\ x\text{ = }\sqrt[]{225} \\ x\text{ = 15 units } \end{gathered}[/tex]
Cosine of the acute angle is calculated as,
[tex]\begin{gathered} \cos (\theta_1)\text{ = }\frac{15}{17} \\ \end{gathered}[/tex]
and
[tex]\cos (\theta_2)\text{ = }\frac{8}{17}[/tex]
Thus the required answer is ,
[tex]\begin{gathered} \cos (\theta_1)\text{ = }\frac{15}{17} \\ \cos (\theta_2)\text{ = }\frac{8}{17} \end{gathered}[/tex]
