Seats on carousel

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:

$n = 12 \ \\ s = 1.5 \ \text{m} \ \\ \ \\ φ = \dfrac{ 360 }{ 2 \cdot \ n } = \dfrac{ 360 }{ 2 \cdot \ 12 } = 15 \ ^\circ \ \\ \ \\ \sin\ φ\ = \ s/2\ :r \ \\ \ \\ r = s/2 / \sin φ = s/2 / \sin 15\degree \ = 1.5/2 / \sin 15\degree \ = 1.5/2 / 0.258819 = 2.89778 = 2.8978 \ \text{m} \ \\ \ \\ \text{ Verifying Solution: } \ \\ o = 2 \pi \cdot \ r = 2 \cdot \ 3.1416 \cdot \ 2.8978 \doteq 18.2073 \ \text{m} \ \\ o_{1} = o/12 = 18.2073/12 \doteq 1.5173 \ \text{m} \ \\ o_{1}\ \ldots\ s$

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