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.
6.65
9.38
To find the lengths of the legs of a trapezoid, we can use the formula for the area of a trapezoid:
Area = ((b1 + b2) / 2) × h
where b1 and b2 are the lengths of the two bases and h is the height of the trapezoid.
However, in order to find the height, we need more information. The given angles at the extremities of the larger base are not sufficient to determine the length of the legs.
If you have additional information about the trapezoid, such as the lengths of the legs or the height, please provide it so that we can find the solution.