Question

A circle has a radius of 7ft. Find the radian measure of the central angle θ that intercepts an arc of length 10ft.

Answer 1

Given:-

• A circle has a radius = 7ft.

• Length of Arc = 10ft.

To Find:-

• Measure of the central angle θ in radians.

Formula Used:-

• ${\boxed{\bf{Length\:of\:Arc=\dfrac{\theta}{360°}\times2\pi r}}}$

Solution:-

Using,

$\bf :\implies\:Length\:of\:Arc=\dfrac{\theta}{360°}\times2\pi r$

$\sf :\implies\:10=\dfrac{\theta}{360°}\times2\times \dfrac{22}{7}\times 7$

$\sf :\implies\:10=\dfrac{\theta}{360°}\times44$

$\sf :\implies\:\theta=\dfrac{10\times360}{44}$

$\sf :\implies\:\theta=\dfrac{10\times90}{11}$

$\sf :\implies\:\theta=\dfrac{900}{11}$

$\bf :\implies\:\theta=81.\overline{81}°$

Now, 81.81° = 1.42 radians

Hence, Measure of the central angle θ in radians is 1.42.

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