Because you have two of the three measurements needed for the sides, let's do side AC first.
Use the hypotenuse formula: a^+b^2=c^2
Plug in as follows: a^2+5^2=13^2
This is one of the common triangle side trifectas, meaning, whenever you see 5 and 13 as sides, the other side will be 12. Thus, side AC is 12.
To find the other angle, we must use a formula. We already know angle c is 90 degrees. You need to use the formula for law of cosines: a^2=b^2+c^2-2bccosA.
So input: 5^2=12^2+13^2-2(12)(13)cosA.
You get 25=144+169-312cosA. Subtract 144 and 169 on both sides.
Your new equation should look like -288=-312cosA.
Divide both sides by -312 to get about .923. Then use cos^-1(.923) to get angle "a" as 22.62 degrees.
Because we already have angle "c" and "a", add the two then subract by 180.
90+22.62= 112.62. 180-112.62 makes angle b 67.38.
