How do you find the radian measure of the central angle of a circle of radius 14.5 centimeters that intercepts an arc of length 25 centimeters?

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Answer 1 · 2018-05-02T16:08:09

Divide the arc length by the radius to get your angular displacement in radians ( $θ = 1.72414 = 0.549 π$ $theta=1.72414=0.549pi$ )

The arc length of a circle, with respect to a given radius and angle, can be written as an equation:

$S = r θ$ $S=rtheta$

Where $S$ $S$ is the arc length, $r$ $r$ is the radius, and $θ$ $theta$ is the angle in radians. Plugging in the values we do know:

$25 = 14.5 θ$ $25=14.5theta$

$θ = \frac{25}{14.5}$ $theta=25/14.5$

$θ = 1.72414 rad$ $color(green)(theta=1.72414" rad")$

if we need to express it in terms of $π$ $pi$ , since radians are (essentially) fractions of $π$ $pi$ :

$θ = 0.549 π rad$ $color(green)(theta=0.549pi" rad")$