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$csc=\frac{hyp.}{oposite}=\frac{5}{3} \\ cos=\frac{adj.}{hyp.}$

so we know hyp=5 and oposite=3 let s use pythagorean theorem to find adj :

3^2+x^2=5^2

x=4  

so your adj is 4 and hyp is 5

$cos=\frac{adj.}{hyp.}=\frac45$