Answer: 36.3m
Explanation:
To solve this, we can draw two triangle rectangles, where the distance between the man and the base of the tower is one of the cathetus, the adjacent one, the height will be the opposite cathetus.
The triangle where the elevation angle is 58° is associated with the height of the tower without the aerial
The other triangle, where the elevation angle is 63° is associated with the height of the tower with the aerial.
Then we can calculate those two heights, then compute the difference, and the difference will be equal to the height of the aerial.
In both cases we want to calculate the opposite cathetus, then we should use the relation:
Tan(θ) = (Op. cath)/(Adj. cath)
The height without the aerial is h1, let's find it:
Tan(58°) = h1/100m
Tan(58°)*100m = h1 = 160m.
The height with the aerial is h2, let's find it:
Tan(63°) = h2/100m
Tan(63°)*100m = h2 = 196.3m
Then the height of the aerial will be:
h2 - h1 = 196.3m - 160m = 36.3m