Question

Find the length of the arc, S, on the circle of radius are intercepted by central angle zero. Express the arc length in terms of X. Then round your answer to two decimal places. Radius, our equals 8 inches; central angle, zero equals 135°. First convert the degree measure into radians. Then use the formula S equals 0R, where S is the arc length zero is the measure of the central angle in radians and are is the radius of the circle

Answer 1

The length of an arc subtended by a central angle and 2 radii is

`S=r\theta`

Where:

r is the radius

Cita is the central angle in radian

Since the radius of the circle is 8 inches, then

`r=8`

Since the arc is subtended by a central angle of 135 degrees, then

`\begin{gathered} \theta=135*(\pi)/(180) \\ \theta=(3)/(4)\pi \end{gathered}`

Substitute them in the rule above

`\begin{gathered} S=8*(3)/(4)\pi \\ S=6\pi \end{gathered}`

The length of the arc is 6pi

We will find it in 2 decimal places

`\begin{gathered} S=6\pi \\ S=18.85 \end{gathered}`

The length of the arc is 18.85 inches