The angle that would subtend an arc of length 6 feet on a circle of radius 5 feet is 68.75°
From the question,
The radius of the circle is 5 feet.
To determine what angle would subtend an arc of length 6 feet,
From the formula for length of an arc, we have that
[tex]l=\frac{\theta}{360^{o} } \times 2\pi r[/tex]
Where [tex]l[/tex] is the length of the arc
[tex]\theta[/tex] is the angle subtended by the arc
and [tex]r[/tex] is the radius of the circle
From the question
[tex]l = 6 feet[/tex]
[tex]r = 5feet[/tex]
To determine measure of the angle, [tex]\theta[/tex]
Put the values into the equation
[tex]l=\frac{\theta}{360^{o} } \times 2\pi r[/tex]
[tex]6=\frac{\theta}{360^{o} } \times 2\pi (5)[/tex]
[tex]6=\frac{\theta}{360^{o} } \times 10\pi[/tex]
Then,
[tex]\theta \times 10\pi = 360 \times 6[/tex]
[tex]\theta =\frac{360 \times 6}{10\pi}[/tex]
[tex]\theta =\frac{2160}{10\pi}[/tex]
[tex]\theta =\frac{216}{\pi}[/tex]
∴ [tex]\theta = 68.75^{o}[/tex]
Hence, the angle that would subtend an arc of length 6 feet on a circle of radius 5 feet is 68.75°
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