hmmmm the number i got with 15.7 Kilometers

diameter = 5 KM
5 x 3.14 = 15.7

look angle going in both directions need to be the same...and its a right triangle. So that means is 45 degrees. We know one of the sides is 9km, and the other side is 3km+diamter of the circle...equals 6.

We're assuming that the triangle needs to be equilateral in order for the east port to be what blocks our sight-line, no?

[QUOTE=SammyG-SD;13625225]look angle going in both directions need to be the same...QUOTE]

this may be a bad assumption...

I don't think it needs to be equilateral..but isoscles.

lol I did it wrong, stupid maths.

right...definitely isosceles, but we're only concerned with the Eastern half of that triangle. If the eastern port is in the line of sight, then it's gotta be 9-9-9sqrt2 which makes the radius 3 and leads to your answer.

Solved it graphically...looks like the diameter is 9. Sides of the triangles are 9 and 12.

I don't think it's that simple, but I may be complicating it. I'm gonna feel dumb when I do all this and get the same answer as someone else.

Interesting that the point that blocks the sight-line is actually north of the east port. Ew.

Is that geometry sketchpad?

Visio

Here's what I did:



Since we know the long side is sqrt(81+((l/pi)+3)^2) you can use end up using similar triangles to come up with a really long expression involving a 4th power equation then I don't remember how to solve those anymore so just cheated graphed on calculator and got same 18.84 that other people got. Guess I just complicated it.

that's some sexiness right there, zach!

I miss the learning aspect, and sometimes I start to miss school, but I know that I'd be tired of it within a week.

Noobs

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Call the diameter of the castle D

Now lets begin at the south gate. 3+D km north is where the soldiers are
You can just see them if you go 9 kilometers east of this gate

Just see them implies that if you go any less than 9 kilometers they'll be hidden by the castle wall. So a tangent to the castle wall drawn from where the soldiers are meets the 'x axis' 9 kilometers to the east. This forms a right angled triangle.

The other relevant information is that the tangent line will be at right angles to a radius, and this distance will be D/2

I'd be inclined to use co-ordinate geometry to solve the problem. We can make it easier if we consider the centre of the circle to be at (0,r), where r=D/2

Let our tangent line be ax+by+c=0

we know that this intercepts the x-axis at (9,0), and the y-axis at (0,3+2r)

put those into the above equation and we get 9a+b(0)+c=0
a(0)+b(3+2r)+c=0

combining we get 9a=-c=3b+2rb

c=-3b-2rb, and a= -c/9 = b/3+2rb/9

so our equation becomes:

x(b/3+2rb/9)+by-3b-2rb=0

divide by b to get
x(1/3+2r/9)+y-3-2r=0

the distance of the centre of the circle is given by the formula

abs[a(0]+b(r)+c]/[sqrt(a^2+b^2)]

=abs[0+1(r)-3-2r]/[sqrt(1/9+4/81r^2 + 4r/27)]

=(3+r)/sqrt() = r (because it is a tangent)

and from there you should be able to solve for r

The length of the wall around the castle is 2*pi*r

/I just pretended to be stupid

please be a level

I like how an engineer can solve this problem much quicker by drawing it than some one trying to remember the formula for tangents....

reminds me when I took my PE test...I think 85% of the problems could be solved or setup to solve by just drawing what we knew.

Well if you're taking a real test, you don't have acces to computers and therefore you cannot do these:

engineering paper FTW

ruler and protractor FTW.

my dad is a PE

my dad is a mathematician, and I am a PE....we have lots of nerd jokes between us.

moar math plz

I just wanna say that my mom and I love your avatar, hurt.

why ty

and thank her

post more please

sorta balances out the gay sex talk from RE