MathDB

In the right trapezoid

ABCD

with

AB \parallel CD, \angle B = 90^o

and

AB = 2DC

. At points

A

and

D

there is therefore a part of the plane

(ABC)

perpendicular to the plane of the trapezoid, on which the points

N

and

P

are taken, (

AP

and

PD

are perpendicular to the plane) such that

DN = a

and

AP = \frac{a}{2}

. Knowing that

M

is the midpoint of the side

BC

and the triangle

MNP

is equilateral, determine:
a) the cosine of the angle between the planes

MNP

and

ABC

. b) the distance from

D

to the plane

MNP

Problem Statement