Mathematics
minaragy
40

what is the length of an arc of an 8" radius circle if the arc measures 45°.

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(1) Answers
kekenunuanitasky2

First, convert the arc measure from degrees into radians: [latex]\mathsf{1^\circ=\dfrac{\pi}{180}~rad~~\Leftrightarrow~~1~rad=\dfrac{180^\circ}{\pi}}[/latex] So, [latex]\mathsf{\theta=45^\circ}\\\\ \mathsf{\theta=45\cdot \dfrac{\pi}{180}~rad}\\\\\\ \mathsf{\theta=\diagup\!\!\!\!\! 45\cdot \dfrac{\pi}{\diagup\!\!\!\!\! 45\cdot 4}~rad}\\\\\\ \mathsf{\theta=\dfrac{\pi}{4}~rad\qquad\checkmark}[/latex] ________ •   length of the arc:   L; •   measure of the arc (in radians):   [latex]\mathsf{\theta=\dfrac{\pi}{4}};[/latex] •   radius:  r = 8''. [latex]\mathsf{L=\theta \cdot r}\\\\ \mathsf{L=\dfrac{\pi}{4} \cdot 8''}\\\\\\ \mathsf{L=\dfrac{\pi}{\diagup\!\!\!\! 4} \cdot \diagup\!\!\!\! 4\cdot 2''}\\\\\\ \mathsf{L=2\pi\,''}\\\\ \mathsf{L\approx 2\cdot 3.14''}\\\\ \boxed{\begin{array}{c}\mathsf{L\approx 6.28''}\end{array}}\qquad\checkmark[/latex] If you're having problems understanding this answer, try seeing it through your browser: http://brainly.com/question/2190890 Tags: arc length radius angle convert degree radian

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