Your proof is correct and very well done
Factors of 38
1, 2, 19, 38
------------------
1×38
2×19
Factors of 59
1, 59
------------------
Common factors for 38 and 59
1 is the only common factor
------------------
GCF of 38 and 59
1 is the both the common and GCF of 38 and 59
The measure is 61 degrees
Find LCD. LCD is 12.
2×4
3×4
8/12 - 7/12
Answer: 1/12
2log10(3) 2log10(5) 5log10(17)
_______ + _______ + _________
17 3 4
=2.06017