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#### karush

##### Well-known member

- Jan 31, 2012

- 2,820

In the figure, the length of the chord $AB$ is $4 \text { cm}$ and the length of the arc is $5\text{ cm}$

View attachment 1713

(a) Find the central angle $\theta$, in radians, correct to four decimal places.

(b) Give the answer to the nearest degree

this problem is intended to be solved by Newton's Method, so I am have ?? as to how to set it up. I thot that using law of cosines would be part of it since

$$\cos{\theta} = \frac{4^2}{a^2+b^2-2ab}$$

or since $a=b=r$

$$\cos{\theta} = \frac{16}{2r^2-1}$$

and

$$\cos^{-1}{\left(\frac{16}{2r^2-1}\right)}=\theta$$

and also $$S=\theta\cdot r$$ for arc length

so this is where I have a flat tire without a spare....

View attachment 1713

(a) Find the central angle $\theta$, in radians, correct to four decimal places.

(b) Give the answer to the nearest degree

this problem is intended to be solved by Newton's Method, so I am have ?? as to how to set it up. I thot that using law of cosines would be part of it since

$$\cos{\theta} = \frac{4^2}{a^2+b^2-2ab}$$

or since $a=b=r$

$$\cos{\theta} = \frac{16}{2r^2-1}$$

and

$$\cos^{-1}{\left(\frac{16}{2r^2-1}\right)}=\theta$$

and also $$S=\theta\cdot r$$ for arc length

so this is where I have a flat tire without a spare....

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