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
\(l=\frac{\theta}{360^{o} } \times 2\pi r\)
Where \(l\) is the length of the arc
\(\theta\) is the angle subtended by the arc
and \(r\) is the radius of the circle
From the question
\(l = 6 feet\)
\(r = 5feet\)
To determine measure of the angle, \(\theta\)
Put the values into the equation
\(l=\frac{\theta}{360^{o} } \times 2\pi r\)
\(6=\frac{\theta}{360^{o} } \times 2\pi (5)\)
\(6=\frac{\theta}{360^{o} } \times 10\pi\)
Then,
\(\theta \times 10\pi = 360 \times 6\)
\(\theta =\frac{360 \times 6}{10\pi}\)
\(\theta =\frac{2160}{10\pi}\)
\(\theta =\frac{216}{\pi}\)
∴ \(\theta = 68.75^{o}\)
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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