Question

In a rhombus with a side of 34, the longer diagonal is 26. Find, to the nearest degree, the larger angle of the rhombus

Answer 1

The numbers do not seem to work out, lol.

A rhombus has diagonals intersect at right-angles.  All four sides of a rhombus are equal.  So we end up with four right-angled triangle with a hypotenuse of 34, and one leg equal to the half (long) diagonal of 13.
This makes the other leg about 31 long, or a diagonal of 62, longer than the "long diagonal" of 26.

I suspect the question should read the longer semi-diagonal is 26.
Based on that, the other leg is sqrt(34^2-26^2)=21.91.
The greater half-angle therefore has a tangent of 26/21.91=1.1867, and the corresponding half-angle is 49.88 degrees.
The larger angle of the rhombus is therefore 2*49.88=99.76 degrees.