A tower is 100 m high. From a point A on the ground, the angle of elevation of the top of the tower is 22 degrees. From a point B on the ground directly opposite to A, the angle of elevation of the to

Let $H$ be the height of the tower, $H = 100$ m.
Let $A$ be Anna's position and $B$ be Bertha's position.
Let $F$ be the base of the tower.
The angle of elevation from Anna to the top of the tower is $\theta_A = 22^\circ$.
The angle of elevation from Bertha to the top of the tower is $\theta_B = 18^\circ$.
Since the girls are on opposite sides of the tower, the total distance between them is the sum of their distances from the base of the tower. Let $d_A$ be the distance from Anna to the base of the tower ($AF$) and $d_B$ be the distance from Bertha to the base of the tower ($FB$).

In the right-angled triangle formed by Anna, the base of the tower, and the top of the tower:

In the right-angled triangle formed by Bertha, the base of the tower, and the top of the tower:

The total distance $D$ is the sum of $d_A$ and $d_B$:

The distance between the girls is approximately $\text{555 m}$.