The wall and the person form two similar right triangles with respect to the foot of the ladder.
One characteristic of similar triangles is that the corresponding sides are at the same ratio.
This means that the ratio between the height of the person and the wall is equal to the ratio of the bases of both triangles.
To make the calculations easier, I will write the height of the person in feet:
1in = 0.0833333..ft
6in=0.5 ft
5ft 6in =5.5ft
You can calculate the height of the wall as follows:
Multiply both sides by 5.5
The height of the wall is 13ft.