Trapezoid Question??????????????????????????????????????????????

Question

ABCD is a trapezoid, DC is parallel to AB, angle A is 60 degrees, and angle C is 45 degrees (they are opposite angles).

AB and AD are 4.


Find DC and BC.

Answer 1

Angle B is 135. Angle D is 120.

Draw an altitude from point A to the extension of CD and call the point of intersection E. Draw a second altitude from point C to the extension of AB and call the point of intersection F. Note that AECF is a rectangle.

ADE is a 30-60-90 triangle, so ED = 2 and AE = 2sqrt(3). Since AECF is a rectangle, CF is also 2sqrt(3).

CFB is a 45-45-90 triangle. Since CF = 2sqrt(3), BF = 2sqrt(3) and BC = 2sqrt(2)sqrt(3) = 2sqrt(6).

To get CD, note that ED + CD = AB + BF. Therefore, 2 + CD = 4 + 2sqrt(3), and CD = 2 + 2sqrt(3).

Answer 2

h = ABsin60
CD = ABsin60/sin45
BC = ABcos60 + CD
CD = 4.898979
BC = 6.898979