Question

what is the length of an arc that subtends a central angle of 75 degrees in a circle whose radius is 5 inches. round off your answer to nearest whole number

Answer 1

Use the next formula to find the length of the arc

`S=r\cdot\theta`

Where r is the radius, theta is the angle in radians and s is the length of the arc.

The first step is to convert the angle from degrees to radians.

`75deg\cdot(\pi rad)/(180deg)=1.31rad`

Now, replace the given values and find the length of the arc

`\begin{gathered} S=5in\cdot1.31rad \\ S=6.55\approx7 \end{gathered}`

The length of the arc is 7 inches.