Question

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?

Answer 1

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Answer:

195 ft

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.