Circular sector

I have a circular sector with a length of 15 cm with an unknown central angle. It is created from a circle with a radius of 5 cm. What is the central angle alpha in the circular sector?

Correct answer:

α =  57.2958 °

Step-by-step explanation:

$$\begin{gathered} o=15\text{cm} \\ 2r+\alpha \cdot r=o=15\text{cm} \\ r=5\text{cm} \\ \beta =(o-2\cdot r)/r=(15-2\cdot 5)/5=1\text{rad} \\ \alpha =\beta \to \text{°}=\beta \cdot \frac{180}{\pi }\text{°}=1\cdot \frac{180}{\pi }\text{°}=57.296\text{°}=57.2958^{\circ }=57°17^{\prime }45" \end{gathered}$$

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