Question

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

Answer 1

115.47 feet

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.