Bonnie R.

asked • 12/08/17# If a playground swing is 8 feet long and it's rider swings through a distance of 9.5 feet, what angle does the swing travel through?

working on degrees, radians, angles, sin, cosine, tangent

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## 2 Answers By Expert Tutors

Arturo O. answered • 12/08/17

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The arc length traveled is 9.5 ft. The radius of the circle is 8 ft. In radians, the subtended angle is

θ = 9.5/8 rad = 1.1875 rad

Convert to degrees:

θ = (1.1875 rad) [(180°)/(π rad)] ≅ 68.04°

Mark O. answered • 12/08/17

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Hi Bonnie,

This should be an arc length problem. Imagine the motion of the swing forming a sector of arclength s and radius r, where the radius is from the pivot point to the seat. Let r = 8 feet and let s, the arc subtended, be 9.5 feet. The arclength formula is s = rθ, where θ is in radians. So, θ = s/r = (9.5 feet) / (8 feet) = 1.19 rad.

We can convert this answer to degrees by θ = 1.19 rad*(180 deg / π rad) = 68.2 deg

Mark

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Andrew M.

^{o }turn is^{o}= 25.133 ft/360^{o}136.1 degrees12/08/17