the longer base of an isosceles trapezoid is 14 feet. the nonparallel sides are each 10 feet long and the length of diagonal is 16 feet. find the measure of a base angle

Answer 1

So we have a trapezoid ABCD, in which
AB=unknown
BC=10,
CD=14
DA=10
and
AC=16.

Sketch the triangle ACD for which the lengths of all three sides are known.
Using the cosine rule, calculate the cosine of A using
cosA=(AC²+AD²-CD²)/(2*AC*AD)
and hence calculate ∠A.