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

I m assuming  the shorter diagonal is 26 units long.

The diagonals of a rhombus are at right angles  and bisect each other so there will be a right angled triangle formed  by the bisection with hypotenuse = 34 and adjacent side = 1/2 * 26 = 13

so cos x  = 13/34 where x = 1/2 of the larger angle  ( recall that the diagonals bisect the vertex angles in a rhombus)

Larger angle  = 2 * 67.52  = 135 degrees to nearest  degree.