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{{ printedBook.courseTrack.name }} {{ printedBook.name }} This relationship can be used to calculate the length or measure of an arc.

The arc length between $A$ and $B$ can be measured using the relationship between the arc length and arc measure. The arc measure is known, $50_{∘},$ and with the radius, $4$ in., the circumference can be calculated. The circumference is given by the formula $C=2πr.$ Therefore, the circumference is: $C=2π⋅4=8π.$ The values for the arc measure and the circumference are now used to find the arc length.$circumferencearc length =360_{∘}arc measure $

SubstituteValuesSubstitute values

$8πarc length =360_{∘}50_{∘} $

Solve for $arc length$

MultEqn$LHS⋅8π=RHS⋅8π$

$arc length=36050 ⋅8π$

CalcQuotProdCalculate quotient and product

$arc length=3.49065…$

RoundDecRound to ${\textstyle 1 \, \ifnumequal{1}{1}{\text{decimal}}{\text{decimals}}}$

$arc length≈3.5$