Answer:
The measure of angle theta is [tex]\theta=2.25\ radians[/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=20\ ft[/tex]
substitute
[tex]C=2\pi (20)[/tex]
[tex]C=40\pi\ ft[/tex]
step 2
Find the measure of angle theta
we know that
The circumference of a circle subtends a central angle of [tex]2\pi\ radians[/tex]
so
using proportion
Find out the measure of the central angle by a length of arc equal to 45 ft
[tex]\frac{40\pi}{2\pi}=\frac{45}{\theta}\\ \\\theta=2*45/40\\ \\ \theta=2.25\ radians[/tex]
