In an isosceles trapezoid, the large base is 3.7 dm, the lateral side is 1.5 dm

In an isosceles trapezoid, the large base is 3.7 dm, the lateral side is 1.5 dm, and the angle between them is 60 degrees. Calculate the midline of the trapezoid.

Since the middle line of a trapezoid is equal to the half-sum of its bases:

m = (ВС + АD) / 2 h,

then it is necessary to calculate the length of its smaller base BC.

Its length is equal to the segment HK, which is located between two heights. In this way:

НК = ВС = АD – АН – КD.

The segments AH and KD are equal, since this trapezoid is isosceles.

To calculate АH, consider the triangle ΔАВH. Let’s apply the cosine theorem:

cos A = AH / AB;

AH = AB · cos A;

cos 60º = 1/2;

AH = 1.5 1/2 = 1.5 / 2 = 0.75 dm;

HK = BC = 3.7 – 0.75 – 0.75 = 2.2 dm;

m = (2.2 + 3.7) / 2 = 5.9 / 2 = 2.95 dm.

Answer: The middle line of the trapezoid is 2.95 in.