AS maths trig help

Is there a right angle in this triangle?

So you have two sides of three, and no angles?

Yeah just given the length of two sides and the question implies that you have to solve for angle DEF to find the exact value of cos DEF

This system isn't constrained enough to produce an answer. I think you need more information.

Hehe yeah the question is a bit harsh lol. Should I just stick with my original answer?

"In triangle DEF, ED = 5cm and EF = 6cm.
Given that sin(∠DEF) = and ∠DEF is acute.
(a) Find the exact value of cos(∠DEF)"

So I did arcsin(2/3) to get 41.8...degrees for the value of angle of DEF. However when I did cos (41.8...) I got 0.74.... I think this is wrong as the question asked for the exact answer but I'm only getting decimals. any tips?

Just use the identity $\cos^2 \theta + \sin^2 \theta \equiv 1$ and the fact that this angle is acute in order to determine the exact cosine value of it.

"In triangle DEF, ED = 5cm and EF = 6cm.
Given that sin(∠DEF) = and ∠DEF is acute.
(a) Find the exact value of cos(∠DEF)"

So I did arcsin(2/3) to get 41.8...degrees for the value of angle of DEF. However when I did cos (41.8...) I got 0.74.... I think this is wrong as the question asked for the exact answer but I'm only getting decimals. any tips?

Maybe my computer didn't display that correctly - is sin theta 2/3?

Their post doesn't say it explicitly, but yes their working would imply this.

ah must've been a mistake on my part. Yeah sin(DEF) = 2/3

Yep so just use the trig identity cos^x2+sinx^2=1. So substitute the value for sin(x) and you can work out cos(x) accordingly.

so what's the answer?

Have you followed the advice given in Reply #9? What do you come up with as the answer?

not sure mate i got a decimal first and then i got 117