Weightloss

[BMAD]

I am a nice round person . I recently enjoyed the benefits of a weightloss program. Accepting money from the weigthloss company, I am going to be one of those handsome people that show you how much weight they have loss by pulling on their waistbands to indicate the fat they used to have. My belt when looped in its old position is now an extra 5 inches to big. When i get on camera and hold my waistband out (with my belt in its old position) how far will it extend from my body?

[bonanova]

Draw a right triangle with vertices at the center of your circular body C, the apex of your extended belt P, and the point where the belt first touches your waist T.

Angle CTP is a right angle. Call THETA the angle PCT.

This is half of the angle between the two points where the belt leaves your waist.

Side CT = r, the radius of your circular waist

Side CP = r + h, where h is the distance your belt extends from your body.

Side PT = r THETA + DELTA/2 where DELTA is the excess length of your belt (5" in this case).

The other DELTA/2 excess belt length is on the other side of the apex.

The following relations hold.

tan THETA = THETA + 2.5/r

We can't solve for THETA unless we know r.

Let's say your waist started out at 40" and has shrunk to 35". Then r = 35/2Pi = 5.57"

Then THETA = .950 radians, or about 54.4 degrees.

cos THETA = r / (r + h) = cos (54.4) = .5815. Call this x.

Finally, h = r (1-x)/x = .7197 r = 4.0088"

[BMAD]

big as in 5 inches too long.

[Rob_Gandy]

2.5 inches.

[bonanova]

I guess we can assume by "round person" that your waistline approximates a circle.

We need to know the original or final size.

RG's answer is the correct one if you reduced down to a zero waist.

I'm looking at this problem assuming you started out as *gasp* 40" waistline..

Edited March 1, 2013 by bonanova
clarification

[ThunderCloud]

I guess we can assume by "round person" that your waistline approximates a circle.

We need to know the original or final size.

RG's answer is the correct one if you reduced down to a zero waist.

I'm looking at this problem assuming you started out as *gasp* 40" waistline..

R.G.'s answer is correct for any size of waist, assuming the waistline of the pants is pinched off to accentuate the difference. The difference in circumference is 5 inches, so the "slack" must be 5 inches long, but doubled over. Its length should therefore be 2.5 inches regardless of original size. No?

[BMAD]

see photo

Edited March 1, 2013 by BMAD

[nakulendu]

the distance is determinate with given facts if you consider a different kind of a belt. Say the belt is a girdle or metal hoop which does not stretch to form a tangent with your shrunk circumference but stays a larger circle touching your current circumference behind. tried to attach a picture in the file

what you are looking for is the difference in the radii Old - new . (R-r).

Which is 5/2 PI.
or 0.795774715 inches

Belts.bmp

[BMAD]

the distance is determinate with given facts if you consider a different kind of a belt. Say the belt is a girdle or metal hoop which does not stretch to form a tangent with your shrunk circumference but stays a larger circle touching your current circumference behind. tried to attach a picture in the file

what you are looking for is the difference in the radii Old - new . (R-r).Which is 5/2 PI.or 0.795774715 inches

I would had assumed the first option of belts because the belt still would have to go through the loops.