To determine the radius of the circle using the portion shown in the picture you have to use the formula to calculate the arc length of the segment.
[tex]s=2\pi r(\frac{\theta}{360})[/tex]
Where
s is the arc length
r is the radius
π is the number pi
θ is the central angle
For the portion of the circle shown in the picture, the arc length is s=15cm and the angle is θ=27º
The first step you have to write the formula in terms of r:
[tex]s=2\pi r(\frac{\theta}{360º})[/tex]
-Divide both sides by 2π
[tex]\begin{gathered} \frac{s}{2\pi}=\frac{2\pi}{2\pi}r(\frac{\theta}{360}) \\ \frac{s}{2\pi}=r(\frac{\theta}{360}) \end{gathered}[/tex]
-Multiply both sides of the expression by the reciprocal fraction of (θ/360), which is (360/θ)
[tex]\frac{s}{2\pi}\cdot\frac{360}{\theta}=r[/tex]
Next, replace the formula with the given arc length and angle and calculate the radius:
[tex]\begin{gathered} r=\frac{s}{2\pi}\cdot\frac{360}{\theta} \\ r=\frac{15}{2pi}\cdot\frac{360}{27} \\ r=31.8\operatorname{cm} \end{gathered}[/tex]
The radius has a measure of 31.8cm
