In an isosceles trapezoid, the larger base is 2.7 m, the side is 1 m. The angle between them is 60 degrees. find a smaller base.

Isosceles is a trapezoid in which the sides are equal: AB = CD. Thus, AH = KD.

Let’s draw two heights ВН and СK.

Since the segment of the larger base, located between the two bases, is equal to the length of the smaller base НК = ВС, then:

BC = AD – AH – KD.

Let us calculate the length of the segment AH. Consider the triangle ΔАВН.

To calculate, we use the cosine theorem, according to which the cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:

cos A = AH / AB;

AH = AB * cos A;

cos 60º = 1/2;

AH = 1 * 1/2 = 0.5 m.

BC = 2.7 – 0.5 – 0.5 = 1.7 m.

Answer: The length of the smaller base is 1.7 m.