Question

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.

Answer 1

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

Answer 2

now, having the height, use either sine or cosine to find the legs.

Answer 3

6.65
9.38