The bases of the rectangular trapezoid are 4cm and 7cm, and one of the corners is 60 degrees

The bases of the rectangular trapezoid are 4cm and 7cm, and one of the corners is 60 degrees. find the large side of the trapezoid.

Let us draw the height CH from the top of the obtuse angle C.

The height divides the larger base into two segments. The length of the segment НD = АD – АН = 7 – 4 = 3 cm.

In the formed right-angled triangle СНD, the angle СНD = 90, the angle НDC = 60, then the angle НСD = 180 – 90 – 60 = 30.

The HD leg lies opposite the angle 30, therefore its length is equal to half the length of the CD hypotenuse.

Then СD = 2 * НD = 2 * 3 = 6 cm.

Answer: The length of the longer side is 6 cm.