Answer:
[tex]\theta=71.6\°[/tex]
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=4\ m[/tex]
substitute the values
[tex]C=2\pi (4)=8 \pi\ m[/tex]
step 2
Remember that
360 degrees subtends the arc of length [tex]8 \pi\ m[/tex] (circumference)
so
by proportion
Find the measure of θ by an arc of length 5 m
assume [tex]\pi=3.1416[/tex]
[tex]\frac{360}{8\pi}=\frac{\theta}{5}\\ \\ \theta=360*5/8\pi \\ \\ \theta=71.6\°[/tex]
