posted by echus .
The bases of a trapezoid are 38 and 17 respectively. The angles at the extremities of the larger base are 57 degrees and 45 degrees. find the two legs.
The total base under the triangles is 21 (38-17)
Let b = the base by the 57° angle
So, the height
h = b*tan 57 = (21-b) tan(45) = 21-b
1.54b = 21-b
b = 8.27
21-b = 12.73
h = 12.73
now, having the height, use either sine or cosine to find the legs.