Answer:
see explanation
Step-by-step explanation:
∠ AOB = 360° - 264° = 96°
The altitude OM bisects ∠ AOB and the base AB
(a)
∠ MOB = 0.5 × 96° = 48°
Using the cosine ratio in right triangle MOB
cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{OM}{OB}[/tex] = [tex]\frac{18}{r}[/tex] ( OB is the radius r of the circle )
Multiply both sides by r
r × cos48° = 18 ( divide both sides by cos48° )
r = [tex]\frac{18}{cos48}[/tex] ≈ 27 cm ( to the nearest cm )
(b)
Using the tangent ratio in the right triangle MOB
tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{MB}{OM}[/tex] = [tex]\frac{MB}{18}[/tex] ( multiply both sides by 18 )
18 × tan48° = MB then
AB = 2 × MB = 2 × 18 × tan48° = 36 × tan48° ≈ 40 cm ( to nearest cm )
