Math CentralQuandaries & Queries


Question from Marlyn:

I have a curved wall with a radius of 6'. I am trying to have a 36" rod made to hang a tapestry and need to figure out the degree measure of the arc.
Can you help me please?

Hi Marlyn,

I drew a diagram of what I think you are describing.$C$ is the centre of the circle, $AB$ is the rod, $D$ is the midpoint of $AB$ and $\theta$ is the measure of the angle $DCA.$

curved wall

$ADC$ is a right triangle so

\[\tan \theta = \frac{1.5}{6}= \frac14\]

and hence

\[\theta = \tan^{-1} \frac14 = 14.036 \mbox{ degrees.}\]

Hence the measure of the angle $BCA$ is very close to 28 degrees.


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