Emir is standing in a treehouse and looking down at a swingset in the yard next door. The angle of depression from Emir's eyeline to the swing set is 31.43°, and Emir is 11 feet from the ground

I guess we want to find the distance between the bottom of the tree and the swingset.

The data we have is:

Emir is 11 m above the ground.

The angle of depression (this is, the angle from the horizontal line that goes through Emir point of view to the actual eyeline) is 31.43°.

We can make a right triangle, where one of the cathetus is 11m, the adjacent angle to this cathetus is the complementary angle to the angle of depression, so we have:

Angle + 31.43° = 90°

Angle = 90° - 31.43° = 58.57°

Now, we can find the distance between the tree and the swingset as the other cathetus of our triangle, we can use the relation:

Tan(angle) = opposite cathetus/adjacent cathetus.

Tan(58.57) = X/11m

Tan(58.57)*11m = X = 17.9m