Question

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

Answer 1

Answer:

$73.7^\circ$

Step-by-step explanation:

$\text{Solution: }\\1.\ \text{OA = OB [Radii of same circle are equal.]}\\\\2.\ \text{Perimeter of OAB = 23cm}\\\text{or, OA + OB + arc.AB = 23}\\\text{or, 7 + 7 + arc.AB = 23}\\\text{or, arc. AB = 9cm}$

$\text{3. Now we have a formula:}\\\text{Angle at center }(\theta^c)=\dfrac{\text{Length of arc}(l)}{\text{Radius of circle}(r)}\\\text{or, }\theta=\bigg(\dfrac{9}{7}\bigg)^c\\\\\text{or, }\theta=\bigg(\dfrac{180}{\pi}\bigg)^\circ\times\bigg(\dfrac{9}{7}\bigg)\ \ \ \ \bigg[\because\ \pi^c=180^\circ \Rightarrow\ 1^c=\bigg(\dfrac{180}\\{\pi}\bigg)^\circ\bigg]$

$\text{or, }\theta\approx73.7^\circ$