Respuesta :
Angles and arcs' lengths are related to each other. The length of the minor arc SV is given by: Option A: [tex]20\pi \: \rm inches[/tex]
How can we use a full rotation?
Whole circumference is covered by 360 degrees rotation.
How to find the relation between angle subtended by the arc, the radius and the arc length?
[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
The complete problem specifies radius of the circle as 24 in. and
θ = 5pi/6
Thus, we get the measurement of the arc length that angle covers as:
[tex]r \times \theta \: \rm inches = 24 \times \dfrac{5\pi}{6} = 20\pi \: \rm inches[/tex]
Thus, the length of the minor arc SV is given by: Option A: [tex]20\pi \: \rm inches[/tex]
Learn more about length of the arcs here:
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