Question

I need help question

Answer 1

The first thing we have to do is identify our data to be able to answer part a and b.

• The circumference of the circle is 97.2cm

`\begin{gathered} C=97.2cm \\ C=2\pi r \\ r=(C)/(2\pi) \\ r=(97.2)/(2\pi) \\ r=15.47cm \end{gathered}`

a)

if we want to find 1/360 the circumference we just multiply our value of the circumference by the value we want to find

`\begin{gathered} C*(1)/(360)=(97.2)/(360) \\ C*(1)/(360)=0.27cm \end{gathered}`

Let us remember that a circle has 360º, that is to say that if we divide by 360 we would be calculating the value of 1º

a) 1/360th of the circumference of the circle is 0.27 cm long. Since an angle then makes a full rotation measures 360 degrees, the measure of the angle in degrees must be 1 degree

b)

To solve b, we have to do the same calculation that we did in point a) but using the circle that is generated if we had the radius of 16.47cm as seen in the figure above

`\begin{gathered} r_2=16.47 \\ C=2\pi r \\ C_2=2\pi(16.47) \\ C_2=103.48cm \end{gathered}`

Now we calculate the value for 1 degree in our new circumference

`\begin{gathered} C_2*(1)/(360)=(103.48)/(360) \\ C_2*(1)/(360)=0.287 \\ \end{gathered}`

Now if the arc gives us 0.287 cm at how many degrees do we calculate how much it corresponds to in our initial circle

`\begin{gathered} 360\to97.2cm \\ arc\text{ }\to0.287cm \\ arc=(360*0.287)/(97.2) \\ arc=1.06cm \end{gathered}`