Question

the length of the longer base of an isosceles trapezoid is 12 cm the length of each side is 5 cm the measure of each acute angle is 37 find the length of the shorterbase

Answer 1

Drop perpendiculars from the ends of the shorter base to the longer base. Each leg of length 5 makes an acute angle 37° with the base, so the horizontal projection of one leg is 5 cos 37°. The total reduction from the longer base is twice that, so

shorter base = 12 − 2(5 cos 37°) = 12 − 10 cos 37° ≈ 4.01 cm.

(Exactly: 12 − 10 cos 37° ≈ 4.0136 cm.)