Question

Find the values indicated. Leave all answers in simplest form.
AC=
OC=
mAB⌢=

Answer 1

Answer :-

In Right ∆OCA , we have,

→ ∠AOC = 60°

→ AO = 6 unit.

→ ∠OAC = 30°

so, In Right ∆OCA,

→ sin 30° = OC/OA

→ (1/2) = OC / 6

→ OC = 3 units. (Ans.)

and,

→ cos 30° = AC/OA

→ (√3/2) = AC/6

→ AC = 3√3 units (Ans.)

also,

→ ∠AOB = 2 * ∠AOC = 2 * 60° = 120°

therefore,

→ Length of Minor Arc AB = (Angle at centre/360°) *2 * π * radius

→ Length of Minor Arc AB = (120°/360°) * 2 * π * 6

→ Length of Minor Arc AB = (1/3) * 12π

→ Length of Minor Arc AB = 4π = 4 * 3.14 = 12.56 units (Ans.)

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