Math CentralQuandaries & Queries


Question from hassan, a parent:

how to draw a curve long 1m with an angle of 22.5?


My interpretation of your question is that you have a section of an arc of a circle which is 1 metre long and subtended by an angle of measure $22.5^{o}.$ To draw the arc you need $r,$ the radius of the circle.


The formula you need is that $a = r \times \theta$ where $a$ is the length of the arc, $r$ is the radius of the circle and $\theta$ is the measure of the angle in radians. You have the measure of the angle in degrees so you need to multiply by $\large \frac{\pi}{180}$ to convert the measure of the angle. Thus

\[a = r \times \frac{22.5 \times \pi}{180}\]


\[1 = r \times \frac{22.5 \times \pi}{180}\]

which gives

\[ r = \frac{180}{22.5 \times \pi} = 2.546 \mbox{ metres.}\]


About Math Central


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina