Question

Help with 1 and 2 and for the answer to be written thank you

Answer 1

Step-by-step explanation:

Part 1:

The formula to calculate the area of a sector is given below as

`A_(sector)=(\theta)/(360)*\pi r^2`

The formula to calculate the length of an arc is given below as

`L_(arc)=(\theta)/(360)*2\pi r`

Part 2:

The given dimensions are

`\begin{gathered} \theta=160^0 \\ r=5in \end{gathered}`

To figure out the length of the arc, we will use the formula below

`\begin{gathered} A_(sector)=(\theta)/(360)2\pi r \\ A_(sector)=(160)/(360)*2\pi*5 \\ A_(sector)=13.96in^ \end{gathered}`

Hence,

The length of the arc will be

`\Rightarrow L_(arc)=13.96\imaginaryI n^`

To figure out the area of the sector, we will use the formula below

`\begin{gathered} A_(sector)=(\theta)/(360)\pi r^(2) \\ A_(sector)=(160)/(360)*\pi(5^2) \\ A_(sector)=34.91in^2 \end{gathered}`

Hence,

The area of the sector will be

`\Rightarrow A_(sector)=34.91\imaginaryI n^2`