Question

Kyle is pulled back on a swing so that the rope forms an angle of 30° with the vertical. The distance from the top of the swing set directly to the ground is 12 feet. Find Kyle’s height off the ground, , when he is in the pulled-back position. Round the answer to the nearest hundredth.
no way to know. I assume the swing is not dragging on the ground when just hanging.

However, assuming the swing chain is x feet long (x < 12), then the swing is hanging 12-x feet off the ground when at rest.

So, for our problem, the swing at 30° is

12-x + x(1-cos30°) feet off the ground.

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