Without using tables or calculator.
sine A = 8/√233
cos A = 13/√233
How to find other trigonometry functions
Tan A = opposite / adjacent
Sin and cos requires hypotenuse and the hypotenuse will require Pythagoras theorem
hypotenuse² = opposite² + adjacent²
where
opposite = 8
adjacent = 13
hypotenuse² = 8² + 13²
hypotenuse² = 64 + 169
hypotenuse² =233
hypotenuse = √233
sine A = opposite / hypotenuse
sine A = 8/√233
cos A = adjacent / hypotenuse
cos A = 13/√233