The length of escalator is 35 meters.
Step-by-step explanation:
Given:
Vertical rise of elevator: 6 meters (opposite of the angle)
Angle of elevation: 10°
Length of escalator: x (hypotenuse)
The length and vertical rise of elevator and the distance between its foot and base of vertical rise along the ground form a right triangle.
Use trigonometric functions to solve for x, the length of elevator:
Sin θ = opposite/hypotenuse
Find the length of elevator, x:
Sin 10° = 6 meters/x
x = (6 meters) / (Sin 10°)
x = (6 meters) / (0.1736)
x ≈ 34.56 meters
x ≈ 35 meters
The length of escalator is 35 meters.
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