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There are 12 seats evenly distributed on the children's carousel in the shape of a circle. How long is the arm of the carousel (connecting the center of the carousel to the seat) if the distance between the two seats is 1.5m?

Correct answer:

r =  2.8978 m

Step-by-step explanation:

$$\begin{gathered} n=12 \\ s=1.5\text{m} \\ \phi =\frac{360}{2\cdot n}=\frac{360}{2\cdot 12}=15{}^{\circ } \\ \sin \phi =s/2:r=1.5/2:2.8978=\infty =0:0 \\ r=s/2/\sin \phi =s/2/\sin 15°=1.5/2/\sin 15°=1.5/2/0.258819=2.89778=2.8978\text{m} \\ \text{ Verifying Solution: } \\ o=2\pi \cdot r=2\cdot 3.1416\cdot 2.8978\doteq 18.2073\text{m} \\ {o}_1=o/12=18.2073/12\doteq 1.5173\text{m} \\ {o}_1\dots s \end{gathered}$$

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