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n escalator in the subway station has a vertical rise of 195 ft 9.5 in., and rises at an angle of 10.4°. How long is the escalator? Round to the nearest foot.

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Khoso123

Answer:

[tex]l=1085ft[/tex]

Explanation:

Since the answer is supposed to be feet convert the inches to feet

[tex]195+\frac{9.5}{12}=195.79ft[/tex]

The angle of rise is at the lower floor,so the vertical rise represents the opposite side of a right triangle.The length of the escalator is then hypotenuse of triangle

[tex]Sin(10.4)=\frac{195.79}{l}\\lSin(10.4)=195.79\\l=\frac{195.79}{Sin(10.4)}\\l=\frac{195.79}{0.18} \\l=1084.7ft\\round-it\\l=1085ft[/tex]

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