Carousel for children

There are 5 seats evenly distributed on the children's carousel in the shape of a circle. What kind the arm of the carousel (connecting the center of the carousel to the seat) is long if the distance between with two seats is 1.2m?

Correct answer:

r =  1.0208 m

Step-by-step explanation:

$$\begin{gathered} n=5 \\ s=1.2\text{m} \\ \phi =\frac{360}{2\cdot n}=\frac{360}{2\cdot 5}=36{}^{\circ } \\ \sin \phi =s/2:r \\ r=s/2/\sin \phi =s/2/\sin 36°=1.2/2/\sin 36°=1.2/2/0.587785=1.02078=1.0208\text{m} \\ \text{ Verifying Solution: } \\ o=2\pi \cdot r=2\cdot 3.1416\cdot 1.0208\doteq 6.4138\text{m} \\ {o}_1=o/12=6.4138/12\doteq 0.5345\text{m} \\ {o}_1\dots s \end{gathered}$$

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