Answer:
80.78°
Step-by-step explanation:
When the 30 cm long string will be bent in the form of a sector it's two sides will be radii of the sector and lower part be the arc. Length of the arc can be found as given below.
Length of the string = 30 cm
radius of sector (r)= 8.8 cm
Length of the arc (l) = 30 - 2*8.8 = 30 - 17.6 = 12.4 cm
Let the sector makes [tex]\theta[/tex] angle at the centre of the circle.
Formula for length of arc of a sector is given as:
[tex]\huge \red{l=\frac{\theta}{360\degree}\times 2\pi r}[/tex]
Plugging the values of l and r in the above formula, we find:
[tex]12.4 = \frac{ \theta}{360 \degree} \times 2(3.14)(8.8) \\ \\\implies12.4 = \frac{ \theta}{360 \degree} \times 55.264 \\ \\ \implies \: \theta = \frac{12.4 \times 360 \degree}{55.264} \\ \\ \implies \: \theta =80.775 \degree \\ \\ \implies \: \theta \approx \: 80.78 \degree[/tex]
