The longer base of an isosceles trapezoid measures 22 ft. the nonparallel sides measure 8 ft, and the base angles measure 75°. find the length of a diagonal.

The length of a diagonal is 21.44 feet ( approximately).

Step-by-step explanation:

Given a trapezoid ABCD

AD= 22 feet

DC=8 feet

AD= DE+EA

Let DE=x and CE= y

In triangle DEC

x= 2.070

DE=x=2.0 feet( approximately)

y=7.7274

y=7.73( approximately)

CE=7.73 feet

EA= AD-DE=22-2=20 feet

In triangle AEC

Usin pythogorous theorem

AC=21.44 feet (approximately)

Hence, the length of diagonal =21.44 feet ( approximately).