Question

a piece of thread of length 21.4 cm is used to form a sector of a circle when the radius is 4.2 cm on a piece of clothes calculate the angle of a sector​

Answer 1

Length of arc, L = 21.4 - 2 x 4.2cm

= 21.4 - 8.4

= 13cm

But L = θ360o x 2πr

i.e 13 = θ360o x 2 x 227 x 4.2

= 13 x 360o x 7

= θ x 2 x 22 x 4.2

θ = 13×360o×744×4.2

= ≈ 177.27o

≈ 177o (to the nearest degree)

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Answer 2

Step-by-step explanation:

circumference = 2 × pi × r

= 2 ×3.142 × 4.2

= 26.3928 cm

circumference = 26.3928 cm = 360 °

So 21.4 cm = ? °

= 360 × 21.4 ÷ 26.3928

= 291.8977903064°

= 292 °

Or

26.3928 ÷ 6 = 4.3988

21.4 ÷ 4.3988 = 4.8649631718 radian