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?

Question

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

Answer 1

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° 

Answer 2

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