A circular arc of length 17 feet subtends a central angle of 40 degrees. Find the radius of the circle in feet.

What I have done is:

$$40/1 * \pi/180 = 2\pi/9$$

$$17 = r * 2\pi/9 $$

$$17 * 9/2\pi = 153/2\pi{\rm~ft}$$

I got $240.33183799961918$ feet

Answer is $24.35070629306$. where did I make mistake? Thanks.

  • 2
    $\begingroup$ You forgot to put parentheses around $2\pi$ when you did the division. $\endgroup$ – Christopher Carl Heckman Apr 5 '16 at 6:45
  • $\begingroup$ How can $\dfrac{153}{2\pi}$ be greater than $153$ ? $\endgroup$ – true blue anil Apr 5 '16 at 6:45

community wiki answer so the question can be closed

Your answer of $\frac{153}{2\pi}~\text{ft}$ is correct. However, when you entered it into your calculator, you failed to put parentheses around the $2\pi$ when you did the division, so you obtained $$\frac{153}{2} \cdot \pi \approx 240.331838$$ rather than $$\frac{153}{2\pi} \approx 24.3507062931$$


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