im abit confused with part a
btw for part b why is tan(90-x) angle QPR tho

For part a, angle PRQ and angle PRS are supplementary angles, because they are next to each other on a straight line in that manner.

This is the most common way that questions involving the supplementary angle rule are asked. A triangle, with a length extended.

In the triangle, we see that cos PRQ = 24/25. Because PRS and PRQ are supplementary angles, this means that PRS = 180 - PRQ.

cos PRS
= cos (180 - PRQ) as detailed above
= - cos PRQ (this is the way the supplementary angle rule is used)
= -24/25

As for part ii, since PRQ = x and PQR = 90, it follows that QPR = 90 - x in the triangle.

So tan (90 - x) is simply tan QPR, where “opp” is QR and “adj” is PQ.

so for a even when they ask for the obtuse angle PRS we can just find PRQ and say it is PRS due to the rule?

You can say that cos PRS = - cos PRQ (but not PRS = PRQ). Yes, this is how it works, and you will see this type of diagrams very often in future.

Oh, one thing. You are not allowed to calculate the value of angle PRQ in attempting to obtain cos PRS. So you cannot do cosine inverse and all those.

thx :)