Trigonometric identity problem from HiSet practice test

[pan90]

We know the answer, but don't know how it makes sense given trigonometric principles.

View attachment 9219

Borrowed from HiSet free practice test

 

[Monoxdifly]

Hint: Tan = height/base

 

[HallsofIvy]

As monoxdifly said, "tangent" is "opposite side over near side". Looking at the right triangle in tne picture, the "opposite side" to the 20 degree angle has length "x" and the "near side" has length 25 feet. tan(20)= x/25 so x= 25 tan(20). But x is the height of the eagle above the person's eye level, not the height of the eagle above the ground. We have to add the 5 feet from the ground 5o the person's eye level.