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Circle O shown below has a radius of 27 inches. Find, to the nearest tenth of adegree, the measure of the angle, 2, that forms an are whose length is 14 inches.

Circle O shown below has a radius of 27 inches Find to the nearest tenth of adegree the measure of the angle 2 that forms an are whose length is 14 inches class=

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SOLUTION

To calculate the value of x the length of arc formula will be used

The formua for length of arc is

[tex]L=\frac{\theta}{360}\times2\pi r[/tex]

From the given circle

L= 14

r=27

Substitute the values into the formula

[tex]14=\frac{x}{360}\times2\pi\times27[/tex]

Solve for x

[tex]\begin{gathered} 14\times360=54\pi x \\ 5040=54\pi x \\ x=\frac{5040}{54\pi} \end{gathered}[/tex]

Hence the value of x is

[tex]x=29.7^{\circ}[/tex]

Therefore the required angle is 29.7⁰

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