Circle section

An equilateral triangle with side 33 is an inscribed circle section whose center is in one of the triangle's vertices, and the arc touches the opposite side.

Calculate:

a) the length of the arc
b) the ratio between the circumference to the circle sector and the perimeter of the triangle

Correct answer:

x =  29.9277 cm
y =  0.3023

Step-by-step explanation:

$$\begin{gathered} a=33\text{cm} \\ r=\frac{\sqrt{3}}{2}\cdot a=\frac{\sqrt{3}}{2}\cdot 33\doteq 28.5788\text{cm} \\ A=60{}^{\circ } \\ x=r\cdot A°\to \text{rad}=r\cdot A°\cdot \frac{\pi }{180}=28.578838324886\cdot 60°\cdot \frac{3.1415926}{180}=29.928=29.9277\text{cm} \end{gathered}$$

$$\begin{gathered} p=3\cdot a=3\cdot 33=99\text{cm} \\ y=\frac{x}{p}=\frac{29.9277}{99}=0.3023 \end{gathered}$$

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