Question 951623
Right Triangle,  A is the unknown angle.  Draw this:
Right triangle, right angle C, narrow angle A, your angle B.  
b is opposite side of B;
1 is opposite side of angle A;


{{{cos(B)=1/sqrt(26)=0.1961}}}
From that, {{{arcos(0.1961)=78.69*degree}}}.   This should be your angle B.


Your angle A should be as {{{sin(A)=1/sqrt(26)=0.1961}}}, and {{{arcsin(0.1961)=11.31*degree}}}.


Simple definitions of sine and cosine for right triangles was used  (and help of scientific calculator).


The angle C is the right angle, 90 degrees.


CHECK:  11.31+78.69+90=180


SUMMARY:
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Angle A, 11.31 degree
Angle B, 78.69 degree
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A drawing would help.


Your expected angle B would seem to be arcos(0.2493)=75.56, but this does not agree with your given "adjascent side" and hypotenuse.