Answer:
[tex]GIF=1.239 R[/tex]
[tex]HET= 3.769 R[/tex]
Step-by-step explanation:
Assuming the image is the shown below, we can use the following formula to find the length of arc [tex]L_{arc}[/tex]:
[tex]L_{arc}=2 \pi R (\frac{\theta}{360 \°})[/tex]
Where [tex]\theta[/tex] is the angle in the arc and [tex]R[/tex] is the radius of the circle.
Since we are not given the value of [tex]R[/tex], we will only work with this.
For [tex]GIF[/tex]:
[tex]L_{arc-GIF}=2 \pi R (\frac{71\°}{360 \°})[/tex]
[tex]L_{arc-GIF}=1.239 R[/tex]
For [tex]HET[/tex]:
We firstly need to find the value of this angle, taking into account the whole circumference is [tex]360 \°[/tex]:
[tex]360 \°=71 \°+53 \°+HET+20 \°[/tex]
Finding [tex]HET[/tex]:
[tex]HET=216 \°[/tex]
Now, let's calculate the length of arc:
[tex]L_{arc-HET}=2 \pi R (\frac{216\°}{360 \°})[/tex]
[tex]L_{arc-HET}=3.769 R[/tex]
