Question

Using the image, determine the length of each arc.

Answer 1

Answer:

$GIF=1.239 R$

$HET= 3.769 R$

Step-by-step explanation:

Assuming the image is the shown below, we can use the following formula to find the length of arc $L_{arc}$:

$L_{arc}=2 \pi R (\frac{\theta}{360 \°})$

Where $\theta$ is the angle in the arc and $R$ is the radius of the circle.

Since we are not given the value of $R$, we will only work with this.

For $GIF$:

$L_{arc-GIF}=2 \pi R (\frac{71\°}{360 \°})$

$L_{arc-GIF}=1.239 R$

For $HET$:

We firstly need to find the value of this angle, taking into account the whole circumference is $360 \°$:

$360 \°=71 \°+53 \°+HET+20 \°$

Finding $HET$:

$HET=216 \°$

Now, let's calculate the length of arc:

$L_{arc-HET}=2 \pi R (\frac{216\°}{360 \°})$

$L_{arc-HET}=3.769 R$