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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?

2 Answers

1 vote

To work out the central angle, you just re-arrange the equation for the length of an arc:

Equation for length of an arc:


(angle)/(360) ×
diameter × π =
length of arc

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]


(q)/(360) ×
10π =
7 (Now just rearrange for q)


(q)/(360) =
(7)/(10\pi ) (multiply both sides by 360 to get q)


q =
(7)/(10\pi ) ×
360 (now just simplify)


q =
(252)/(\pi )

=
80.214 (rounded to 3 decimal places)

______________________________

Therefore:

The equation that gives you ange q is:


q =
(length.of.arc)/(diamater.times.\pi ) ×
360

and q = 80.214 when all of the values are substituted in.

User Kevin Kuszyk
by
8.4k points
2 votes

Answer:

B q=7/5

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

User Kerrith
by
8.7k points

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