a man 1.83m tall, stands at a distance of 14.8m away from the base of a tower. He discovers that the angle of elevation of the top of tower is 63. Calculate the height of the tower.

Answer 1

I assume you mean that the angle of elevation is from the man's eye-level, or what does his height matter? Also, his eye-level can be approximated by his height.

If so, then draw a diagram, as always. Then check your basic trig functions. It should be clear that the desired height h can be found using
(h-1.83)/14.8 = tan63°

Answer 2

h1 = 1.83 m.

Tan63 = h2/14.8.
h2 = 14.8*Tan63 =

h = h1+h2 = ht. of tower.