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Could I find the two missing angle measures if I know some of the side lengths of a right triangle? I made my own example... im just not sure how to use TAN, COS, or SIN to solve it.

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Yes. Fist use the Pythagorean Theorem\[a ^{2}+b^{2}=c ^{2}\] to find the measure of side AB. The use Cos(A)=ADJ/Hyp or Sin(A)=opp/hyp and use the inverse sine or cosine functions \[\sin^{-1} opp/hyp\] and that will give you the measure of A then do the same for angle B
3^2+5^2\[3^{2}+5^{2}=c ^{2}\] \[9+25=c ^{2}\] solve for c \[36=c^{2}\] \[c=6\] \[Sin(A)=\frac{ 3 }{ 6 }\] \[\sin^{-1} (\frac{ 3 }{ 6 })=A\] just plug into your calculator

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Thankyou! :)

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