Amother gazes out a second-floor window at her son playing at the playground. if the mother's eye level is 12.6 meters off of level ground and the playground is 20 meters from the base of the building, what is the angle of depression from the mother's line of sight to the playground?

The  arrangement of mother's eye level, ground level and playground forms a right angles triangle.
The legs of this triangle are 12.6 m (eye level to ground) and 20 m (building to playground).

Using trigonometry and assuming the depression angle is Ф;
tan Ф = 20/12.6 = 1.5873
Ф = tan ^-1(1.5873) = 57.78°