Trigonometry

Hi, please can i have help on this question? I don’t understand how to work out the exact values as a fraction because I’m putting the answer into my calculator and I’m getting a decimal. Is there another way to do this?

Here is the question: https://app.gemoo.com/share/image-annotation/592088925576683520?codeId=Ml2ndjmVNQYqE&origin=imageurlgenerator

Thank you!

Just draw a simple right triangle.
tan(alpha) = opp/adj = 2/5
so you can use pythagoras to work out the third side (hypotenuse) and write down cos(alpha).

The relationships can be "learnt" but its just as easy to draw a right triangle each time and work it out.