Math CentralQuandaries & Queries


Question from Larissa, a student:

In a circle, the length of a chord AB is 4 cm and the length of the arc AB is 5 cm. Find the central angle theta, in radians, correct to four decimal places. Then give the answer to the nearest degree. I think I'm supposed to use Newton's method, but am not sure how to start with this problem.

Hi Larissa,

arc and chord

If the radius of the circle is r cm then you know that the length of the arc a is given by

a = r θ

Also from the diagram

sin(θ/2) = 2/r

Solve this equation for r and substitute into the first equation with a = 5. Now you can apply Newton's Method.

If you need more assistance write back,

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