Central angle calculation

There is a circle with a radius of 10 cm and its chord, which is 12 cm long. Calculate the magnitude of the central angle that belongs to this chord.

Final Answer:

α =  73.7398 °

Step-by-step explanation:

$$\begin{gathered} r=10\text{cm} \\ t=12\text{cm} \\ \sin \alpha /2=\frac{t/2}{r} \\ {\alpha }_1=2\cdot \arcsin (\frac{t/2}{r})=2\cdot \arcsin (\frac{12/2}{10})\doteq 1.287\text{rad} \\ \alpha ={\alpha }_1\to \text{°}={\alpha }_1\cdot \frac{180}{\pi }\text{°}=1.287\cdot \frac{180}{\pi }\text{°}=73.74\text{°}=73.7398^{\circ }=73°44^{\prime }23" \end{gathered}$$

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