Explanation:
as always, the sum of all angles in a triangle is always 180°.
therefore, the angle at B is
B = 180 - 27 - 90 = 63°.
for the missing sides we use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides are always opposite of the related angles.
so,
AB/sin(90) = 12/sin(27)
since sin(90) = 1, we have
AB = 12/sin(27) = 26.43227118... ≈ 26.4
AC/sin(63) = 12/sin(27)
AC = 12×sin(63)/sin(27) = 23.55132607... ≈ 23.6