Question

Hi pls help me tysm :)​

Answer 1

80.78°

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
`\theta` angle at the centre of the circle.

Formula for length of arc of a sector is given as:

`\huge \red{l=(\theta)/(360\degree)* 2\pi r}`

Plugging the values of l and r in the above formula, we find:

`12.4 = ( \theta)/(360 \degree) * 2(3.14)(8.8) \\ \\\implies12.4 = ( \theta)/(360 \degree) * 55.264 \\ \\ \implies \: \theta = (12.4 * 360 \degree)/(55.264) \\ \\ \implies \: \theta =80.775 \degree \\ \\ \implies \: \theta \approx \: 80.78 \degree`