Two men on the same side of a tall building notice the angle of elevation to the top Of the building to be 30 and 60 respectively. I f the height of the building is known to be h = 100, find the distance between the two men

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.