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 respectivel

Question

3 years ago

10

y. I f the height of the building is known to be h= 100, find the distance between the two men

1 answer:

Vladimir [108] · Answer 1 · 2022-01-03T20:14:17+03:00

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.