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| Math Central | Quandaries & Queries |
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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,
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,
Harley
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