The angle of elevation to the top of a tower from point a on the ground is 18.6 degrees . from a point​ b, 39.3 feet closer to the​ tower, the angle of elevation is 21.4 degrees . what is the height of the​ tower

this description would make two triangles on the same side of a pole. 

to find one of the other angles in the triangle, (the one between the ground and angle b)

180 - 21.4
= 158.6

the third angle would then be 
180 - 158.6 - 18.6
= 140

you could then use the sine law to solve for the hypotenuse

c/158.6 = 39.3/140
140x = 6232.98
c = 6232.98/140
c = 44.5

then you would need to solve for the hypotenuse of the right angle triangle

c/18.6 = 44.5/158.6
158.6c = 827.7
c = 827.7/158.6
c = 5.2

then you can use sin21.4 = a/5.2 to solve for the height of the tower

sin21.4 = a/5.2
sin21.4(5.2) = a
1.9 = a

therefore the height of the tower is 1.9 feet