Let O be the point of observation.
Let AB be the unfinished tower.
Let AC = H and AB = h
OA = 75 m
∠AOB = 30° and ∠AOC = 60°
From figure:
To find: Height of BC
From right △ABS:
tan 30° = AB/OA
1/√3 = h/75
or h = 25√3
Again, from right △AOC:
tan 60° = AC/OA
√3 = H/75
or H = 75√3
Now,
From figure, BC = H – h
BC = 75√3 – 25√3 = 50√3 = 86.6
The required height is 86.6 meters.