A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which
equation gives the measure of the central angle, q?

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