Question

What is the arc length of an arc with radius 10 in and central angle 60 degrees ? Show your work.

Answer 1

`\\ \sf\longmapsto \ell=(\Theta)/(180)\pi r`

`\\ \sf\longmapsto \ell=(60)/(180)* 3.14(10)`

`\\ \sf\longmapsto \ell=(1)/(3)(31.4)`

`\\ \sf\longmapsto \ell=10.4m`

Answer 2

`\huge \boxed{ \boxed{ \red{{s \approx \: 10.47}}}}`

Explanation:

to understand this

you need to know about:

• geometry
• PEMDAS

tips and formulas:

• 
  `s = \frac{\pi {r} \theta}{180}`

given:

• r=10
• 
  `\theta = 60`

let's solve:

1. 
   `\sf sustitute \: the \: value s \: of \: \theta \: and \: r : \\ =(\pi * 10 * 60)/(180)`
2. 
   `\sf rediuce \: 60 : \\ =\frac{\pi * 10 * \cancel{60} \: ^(1) }{ \cancel{180} \: \:^(3) } \\ =(\pi * 10)/(3)`
3. 
   `\sf use \: 3.14 \: for \: \pi : \\ = (3.14 * 10)/(3)`
4. 
   `\sf simplify \: multipication : \\ = (31.4)/(3) \\ \approx \: 10.47`