A piece of thread of length 21.4cm is used to form a sector ...
A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take π=227]
A.
170o
B.
192o
C.
177o
D.
182o
Correct answer is B
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)