Answer: 79.38° (choice A)
Work Shown:
We can use the law of cosines to determine angle A.
a^2 = b^2+c^2-2*b*c*cos(A)
27^2 = 19^2+23^2-2*19*23*cos(A)
729 = 890-874*cos(A)
729-890 = -874*cos(A)
-161 = -874*cos(A)
cos(A) = -161/(-874)
cos(A) = 0.18421053
A = arccos(0.18421053)
A = 79.38489193
A = 79.38
Your calculator needs to be in degrees mode.
The notation "arccos" refers to arccosine. It is the same as inverse cosine, aka
A tool like GeoGebra can be used to confirm the answer is correct.