Question

OAB is a sector of a circle. perimeter of OAB is 23cm, calculate the central angle, θ , in the degrees to 1 d.p.

Answer 1

well, we know the perimeter is 23 cm, and we know the radius of that circle is 7 cm, so hmmm if we subtract both radii, namely 7 + 7 from 23, we're left with 23 - 14 = 9 cm, meaning the arc alone is 9 cm.

`\textit{Arc's Length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=7\\ s=9 \end{cases}\implies 9=\cfrac{\theta \pi (7)}{180}\implies \cfrac{180}{\pi 7}\cdot 9=\theta\implies 73.7\approx \theta`