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Alisiya [41]
3 years ago
10

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

y. I f the height of the building is known to be h= 100, find the distance between the two men
Mathematics
1 answer:
Vladimir [108]3 years ago
4 0

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.

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