# Finding the Distance Between A Point in the Circumference and a Point in the Radius

Two people A and B started to walk from the same point on the circumference of a circle whose radius is 300m; each person walking at the rate of 120m/min. If A walks toward the center of the circle and B along the circumference, what will be the distance of the two people after one minute?

Ok lets get the Angle Walked by Person B.

$${ \frac sr = \theta * 2 \times pi \times r}$$

Where

$${ s = 120 }$$ $${ r = 300 }$$

Therefore

$${ \theta = 22.918 }$$

Lets use Cosine Law to Determine Distance:

$${ c^2 = a^2 + b^2 -2ab \cos \theta}$$ $${ a = 300 - 120 = 180 }$$ $${ b = 300 }$$

I am only getting 432.679

Am I using the formulas incorrectly? What am I doing wrong?

• Area seems to have nothing to do with the problem. Maybe use coordinate geometry. Let the centre of the circle be the origin, and suppose they both start at $(300,0)$. Where is A after $1$ minute? Where is B? – André Nicolas Jul 13 '15 at 2:57
• 1) Find $\theta$, the angle subtended by the 120 arc at the center. 2) Apply cosine law to the triangle with sides 300 and 180, and angle = $\theta$. – Mick Jul 13 '15 at 4:03
• @Mick edited question! but im still not getting it – james Jul 13 '15 at 4:49
• Your got help from @joriki – Mick Jul 13 '15 at 9:09

Your formula ${ \frac sr = \theta * 2 \times pi \times r}$ is wrong, as you can see from the fact that the left-hand side is dimensionless and the right-hand side has dimensions of length.
The correct formula is $\frac sr=\theta$, which is in fact how measuring angles in radians is defined. You can see that this has the right proportionality factor from the fact that it's $2\pi$, a full circle, when $s=2\pi r$.
So $\theta=120/300=0.4$. The value you write happens to be the correct value in degrees, even though that doesn't come out of the equation you write, you don't indicate that it's in degrees, and you appear to have used it as an angle in radians in applying the cosine law. If you use the correct angle ($0.4$ in radians, or your value in degrees), you get the correct result.