To work out the central angle, you just re-arrange the equation for the length of an arc:
Equation for length of an arc:
× × π =
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
<em>[Substitute in]</em>
× π = <em>(Now just rearrange for q)</em>
= (<em>multiply both sides by 360 to get q)</em>
= × <em>(now just simplify)</em>
=
= <em>(rounded to 3 decimal places)</em>
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Therefore:
The equation that gives you ange q is:
= ×
and q = 80.214 when all of the values are substituted in.