Finding the distance from a circle.

[jwpaine]

This, like much of the stuff I think about, is not school related. I got thinking about this problem and am trying to figure it out with very little, to no, calculus experience. I drew my problem up in paint.

I don't want the answer... I just want to be pointed in the right direction....Or maybe I'm onto it?

Lets say my circle is 1000 units in circumference. My rocket leaves a single point on my circle at 45 degrees. The distance from A to B is 1000 units, and B is where my ship stops.

What would the length of CB be.


To get CB straight on to the earth....I drew a line from B, through C and through the center of my circle.


This is what I am thinking of doing..tell me if I have the right idea.

If my circumference is 1000 units, and the piece of pie that is A-C and the center of my circle is a fraction of the total area of my circle... then I can find the distance from A to C that is a fraction of the total circumference?

When I know AC, then I can use trig to find BC.

Am I on the right direction to finding BC?

Thanks.

 

[Denis]

Let M = center of that circle of yours.

Now lets look at triangle ABM:
angle BAM = 135 degrees
AB = 1000
AM = radius of circle = 500 / pi

Correct?
If so, you can calculate BM easily; then BC = BM - 500 / pi;
then you can calculate AC; so yer all set...

IF the AC you're talking about is arc AC (not length AC),
then it's simpler: use angle AMB, which can be calculated after getting BM.

 

[jwpaine]

Ahh... Of course!

a^2 = b^2 + c^2 -2bc * cos(A)

c = opposite angle M

a^2 = 160^2 +1000^2 -2(160)(1000)Cos(135)
a^2 = 1251870
BM = a = 1118.87
BC = 1118.87 - 160 = 958.87




Thank you!

 

[TchrWill]

Lets say my circle is 1000 units in circumference. My rocket leaves a single point on my circle at 45 degrees. The distance from A to B is 1000 units, and B is where my ship stops.

What would the length of CB be.


This, like much of the stuff I think about, is not school related. I got thinking about this problem and am trying to figure it out with very little, to no, calculus experience. I drew my problem up in paint.

I don't want the answer... I just want to be pointed in the right direction....Or maybe I'm onto it?

From your figure (letting the center ofthe circle be O, the radius, AO, of the circle with circumference = 1000 is R = 1000/Pi = 318.3 units.

AB = 1000 units.

From triangle ABC, angle CAB= 135º.
'Use the Law of Cosines to find OB and subtract 318.5 to get CB.