Question

I need help with these questions. Please show workings.​

Answer 1

see explanation

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° =
`(adjacent)/(hypotenuse)` =
`(OM)/(OB)` =
`(18)/(r)` ( OB is the radius r of the circle )

Multiply both sides by r

r × cos48° = 18 ( divide both sides by cos48° )

r =
`(18)/(cos48)` ≈ 27 cm ( to the nearest cm )

(b)

Using the tangent ratio in the right triangle MOB

tan48° =
`(opposite)/(adjacent)` =
`(MB)/(OM)` =
`(MB)/(18)` ( multiply both sides by 18 )

18 × tan48° = MB then

AB = 2 × MB = 2 × 18 × tan48° = 36 × tan48° ≈ 40 cm ( to nearest cm )