Find the angles of the MPKC trapezoid, if its bases are 12 and 26 m, the side of the PM = 10 m, the height of the PH = 8 m.

Let’s build the heights РH and KЕ.

In a right-angled triangle МРH, according to the Pythagorean theorem, МH ^ 2 = МР ^ 2 – РH ^ 2 = 100 – 64 = 36.

MH = 6 m.

Quadrangle РKЕH rectangle, HE = РK = 12 m.

Then EC = MC – MH – HE = 26 – 6 – 12 = 8 m.

In a right-angled triangle EKC, leg EK = EC = 8 cm, then the angle ECK = EKC = 45, then the angle CKP = 90 + 45 = 135.

In a right-angled triangle MPH, SinM = PH / PM = 8/10 = 0.8.

Angle PMH = arcsin0.8 = 53.

Then the angle MPK = 180 – 53 = 127.

Answer: The angles of the trapezoid are 45, 53, 127, 135.