Posted by **me** on Monday, March 18, 2013 at 7:18am.

A goat is tied at point A with a rope of length(L). How long can L be so that the goat can feed on exactly half of the field if the field is a circle.

- urgent maths pls -
**Steve**, Monday, March 18, 2013 at 10:09am
Assuming A is on the edge of the field (circle F), let the radius of the field be R, and the rope be length L.

Let the circle with radius L and center A intersect the field at points B and C.

Then we want the area enclosed by the arcs BC to be 1/2 pi R^2.

The sector of circle A subtended by arc BC has area 1/2 L^2 θ where θ subtends BC.

The rest of the area comprises two segments of circle F, where each has area

1/2 R^2 (φ - sinφ)

where φ subtends arc AB or AC.

So, we want

1/2 L^2 θ + R^2 (φ - sinφ) = pi/2 R^2

So, what are θ and φ?

In triangle FAB, let FB be s.

s^2 = L^2 + R^2 - 2RL cos θ/2

s/sin θ/2 = L/sinφ

That should yield the result you need.

- urgent maths pls -
**me**, Monday, March 18, 2013 at 10:45am
Pls d answer isn't really clear. And where did d triangle come from??

## Answer this Question

## Related Questions

- math - mrs.blalock tied her goat with a 12-foot rope to a stake in the field.the...
- Math - A goat is tethered (tied up) to a stake in the ground with a 5 m rope. ...
- Geometry - Zoe the goat is tied by a rope to one corner of a 15 meter-by-25 ...
- Geometry - Zoe the goat is tied by a rope to one corner of a 15 meter-by-25 ...
- geometry - Zoe the goat is tied by a rope to one corner of a 15 meter-by-25 ...
- Math - A goat is tethered to a stake in the ground with a 5 m rope. The goat can...
- math - A horse is tied to a post by a rope, 8m long at one corner of a ...
- math - a rectangu7loar field is to be enclosed with exactly 240 meters of ...
- Maths - A rectangle field is twice as long as its width and is surrounded by a ...
- math - The Harveys keep their goat on a 3-meter chain connected to a metal hook ...

More Related Questions