Question 1135106
<br>
The instruction "calculate ADC" is very poorly stated, and not clear.  The only interpretation that seems to make sense is it means "determine the measure of angle ADC".  So I will assume that is the question....<br>
Here is a diagram: right angles at B and C; AB=5 and DC=12.<br>
I've added point E on DC to make ABCE a rectangle.<br>
{{{drawing(400,200,-2,16,-2,6,
line(0,0,12,0),line(12,0,5,4),line(5,4,0,4),line(0,4,0,0),line(5,0,5,4),
locate(0,-.5,C),locate(12,-.5,D),locate(5,5,A),locate(0,5,B),locate(5,-.5,E)
)}}}<br>
The area of the trapezoid, 34, is the height, BC, times the average of the tow bases, AB and CD.  Given AB=5 and CD=12, the height of the trapezoid is 4.<br>
With AB=CE=5 and CD=12, DE=7; then with AE=BC=4, the measure of angle ADC is<br>
{{{arctan(4/7)}}}