urgent maths pls
posted by me on .
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.
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.
Pls d answer isn't really clear. And where did d triangle come from??