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lakkis [162]
3 years ago
9

Marcos is flying a kite 35 feet above an oak tree. The angle of elevation to the top of the tree is 16 degrees and the angle of

elevation to the kite is 25 degrees. What id the distance, b, to the nearest foot marcos is standing from the tree?
Mathematics
1 answer:
Elza [17]3 years ago
3 0

9514 1404 393

Answer:

  195 ft

Step-by-step explanation:

The relationship between the horizontal distance, angle, and vertical height is given by ...

  Tan = Opposite/Adjacent

Referring to the attached diagram, we have ...

  tan(16°) = BT/MB

  tan(25°) = BK/MB

Solving for BT and BK, we can describe their difference as ...

  BT = MB·tan(16°)

  BK = MB·tan(25°)

  BK -BT = 35 = MB(tan(25°) -tan(16°))

Dividing by the coefficient of MB gives ...

  MB = 35/(tan(25°) -tan(16°)) = 35/0.179562

  MB = 195 . . . feet

Marcos is standing 195 feet from the base of the tree.

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