I cannot work out how I should approach a particular problem
involving loci.The question is there is a horse tethered on a rope.
The horse is tethered to the side of a barn which is 20m x 10m.
The horse is tethered at the mid point of the 20m side of the barn
i.e. 10m in. The question is how long should the rope on the tether
be if the horse can graze an area of 150m squared. I'm not sure
how to approach this involving loci and hypoteneuse etc? Are there
any pointers you can give me please? Thanks
If you try to picture this poor horse in its field
tethered to the barn you can see the shape of the area that it can
graze is a semi-circle PROVIDED that the rope is less than 10m long.
(if the rope is over 10m long then the shape is more complicated.
So, if we stick with a semi-circle for the moment and ask the question
"How long would the rope have to be to allow the horse to graze
150m squared?" The formula for the area of a circle is pi*r^2. (for
us, r is the length of the tether.) (^2 = squared) The formula for
the area of a semi-circle is therefore 1/2*(pi*r^2). So you have
to solve the following equation and hope that the answer is less
than 10m. 1/2*(pi*r^2) = 150 If the answer is more than 10 then
you have a more complicated problem on your hands and I haven't
been able to find an easy answer to that one yet.
Brian
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