In a rectangular trapezoid, the angle C is 120 degrees. CD = 20 cm, MN is the midline

In a rectangular trapezoid, the angle C is 120 degrees. CD = 20 cm, MN is the midline of this trapezoid, MN = 7 cm. Find the base of the trapezoid.

1. We calculate the value of the angle ADC:

360 ° – 90 ° – 90 ° – 120 ° = 60 °.

2. For the convenience of calculations, we denote: AD – a, BC – b, CD – c, the angle between c and a – α.

3. We apply the formula for calculating the length of the bases of the trapezoid through the side and the angle between this side and the lower base:

a = b + c x cos α;

a – b = c x cos 60 ° = 20 x 1/2 = 10;

4. MN = (a + b) / 2; a + b = 7 x 2 = 14;

5. We solve the system of equations:

a + b = 14;

a – b = 10;

Add up the equations:

2a = 24;

a = 12;

h = 14 – 12 = 2.

Answer: BC = 2 cm, BP = 12 cm.