step 1
Find out the measure of angle A
we have that
In the given right triangle
[tex]\begin{gathered} cosA=\frac{17}{38}\text{ ----> by CAH} \\ \\ A=cos^{-1}(\frac{17}{38}) \\ A=63^o \end{gathered}[/tex]
step 2
Find out the measure of angle C
Remember that
In the right triangle
A+C=90 degrees -----------> by complementary angles
[tex]\begin{gathered} 63^o+C=90^o \\ C=90^o-63^o \\ C=27^o \end{gathered}[/tex]
