Angle c = 90°side cb = 5side ab = 13find the measures of the following items using whatever method you'd like. show work for full credita. measure of angle a to the nearest degreeb. measure of angle b to the nearest degreec. measure of side ac to the nearest whole number

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.