Question

You are given the circumference of the circle and the measure of the central angle ACB. Find the length of arc AB.circumference = 36 feet; m ZACB= 40"The length of arc AB isfeet

Answer 1

the length of arc ACB is 4 ft

Step-by-step explanation

the length of an arc is given by:

`l=\frac{\theta}{360\text{ \degree}}2\text{ }\pi r`

where l is the length or the arc, theta is the angle in degrees, r is the radius

so

Step 1

find the radius of the circle

`\begin{gathered} 2\text{ }\pi r=36 \\ \text{divide boths ides by 2}\pi \\ \frac{2\text{ }\pi r}{2\text{ }\pi}=(36)/(2\pi) \\ r=(18)/(\pi) \end{gathered}`

Step 2

now, replace in the formula

Let

angle= 40 °

`\begin{gathered} l=\frac{\theta}{360\text{ \degree}}2\text{ }\pi r \\ l=\frac{40}{360\text{ \degree}}2\text{ }\pi((18)/(\pi)) \\ L=(40)/(360)\cdot36 \\ l=4\text{ } \end{gathered}`

therefore, the length of arc ACB is 4 ft

I hope this helps you