Respuesta :
To work out the central angle, you just re-arrange the equation for the length of an arc:
Equation for length of an arc:
[tex]\frac{angle}{360}[/tex] × [tex]diameter[/tex] × π = [tex]length of arc[/tex]
We can arrange this to work out the central angle, q. But first, lets substitute in all of the values that we know:
angle = q
diameter = 5 x 2 = 10 ft
length of arc = 7
[Substitute in]
[tex]\frac{q}{360}[/tex] × [tex]10[/tex]π = [tex]7[/tex] (Now just rearrange for q)
[tex]\frac{q}{360}[/tex] = [tex]\frac{7}{10\pi }[/tex] (multiply both sides by 360 to get q)
[tex]q[/tex] = [tex]\frac{7}{10\pi }[/tex] × [tex]360[/tex] (now just simplify)
[tex]q[/tex] = [tex]\frac{252}{\pi }[/tex]
= [tex]80.214[/tex] (rounded to 3 decimal places)
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Therefore:
The equation that gives you ange q is:
[tex]q[/tex] = [tex]\frac{length.of.arc}{diamater.times.\pi }[/tex] × [tex]360[/tex]
and q = 80.214 when all of the values are substituted in.
Answer:
B q=7/5
Step-by-step explanation:
Well Q=s/r and they said a Radius of 5 Which puts 5 at the bottom.
Then an arc length of 7 Which =S. so q=7/5