If a an arc of length 5.5 yards subtends a central angle of 0.5 radians on a circle, then the radius of the circle has length: How many yards?

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If a an arc of length 5.5 yards subtends a central angle of 0.5 radians on a circle, then the radius of the circle has length: How many yards?

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Answer 1 · 2018-03-14T10:14:31

radius $r = 11 y a r d s$ $r=11 yards$ .

Explanation:

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First convert the radians into degrees.
$1 r a d = (\frac{180}{π}) d e g r e e s$ $1 rad=(180/pi)degrees$
$0.5 r a d = 0.5 \cdot (\frac{180}{π}) d e g r e e s = (\frac{90}{π}) d e g r e e s$ $0.5 rad=0.5*(180/pi)degrees=(90/pi)degrees$
$\frac{θ}{360} \cdot 2 π r =$ $theta/360*2pir=$ length of an arc, where, $θ$ $theta$ is the angle subtended by the arc in degrees.
Thus, plugging in the values in the equation,
we get:
$(\frac{90}{π}) \cdot \frac{1}{360} \cdot 2 \cdot π \cdot r = 5.5$ $(90/pi)*1/360*2*pi*r=5.5$ yards
Simplify that to get:
$(\frac{r}{2}) = 5.5$ $(r/2)=5.5$ yards
$r = 5.5 \cdot 2$ $r=5.5*2$ yards
$= 11 y a r d s$ $=11 yards$

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If a an arc of length 5.5 yards subtends a central angle of 0.5 radians on a circle, then the radius of the circle has length: How many yards?

1 Answer

Explanation:

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