First, we need to find the height of point A, which is where Angel is standing. We can use the tangent function to do this:
tan(38°) = height of point A / 21 meters
height of point A = 21 meters * tan(38°) = 14.1 meters
Next, we need to find the distance from point A to point B. We can use the tangent function again, this time with the angle of elevation from point A to point B:
tan(46°) = distance from point A to point B / 21 meters
distance from point A to point B = 21 meters * tan(46°) = 20.8 meters
Finally, we can add the height of point A and the distance from point A to point B to get the height of the antenna:
height of antenna = height of point A + distance from point A to point B + height of Angel's eyes
height of antenna = 14.1 meters + 20.8 meters + 1.66 meters = 36.56 meters
Therefore, the height of the antenna is approximately 36.6 meters.