Answer:
115.47 feet
Step-by-step explanation:
You know the relation between opposite and adjacent sides of an angle in a right triangle is ...
Tan = Opposite/Adjacent
If the "adjacent" side of the angle of elevation is the distance of the man from the building, we have ...
tan(30°) = (100 ft)/d1
and
tan(60°) = (100 ft)/d2
Solving these equations for d1 and d2 gives ...
d1 = (100 ft)/tan(30°)
d2 = (100 ft)/tan(60°)
Then the distance between the two men is ...
d = d1 -d2 = (100 ft)(1/tan(30°) -1/tan(60°)) ≈ 115.47 ft
The distance between the two men is about 115 feet.
