The longer base of an isosceles trapezoid measures 23 ft. the nonparallel sides measure 9ft, and the base angle measure 80 degrees. find the length of a diagonal.

We can start with an altitude of a trapezoid:
h = 9 * sin 80° = 9 * 0.9848 = 8.86 ft.
Then look at the right triangle, where a hypotenuse is 9 and one leg is 8.86. Another leg is x.
x² = 9²- 8.86²
x² = 81 - 78.4996
x = √ 2.5004
x = 1.58
23 - 1.58 = 21.42
Finally the diagonal:
d² = 21.42² + 8.86² = 458.8 + 78.4996 = 537.3
d = √537.3 = 23.18 ≈ 23 ft
  D.  23 ft.