Given a circle with radius of 2, which is the degree measure of an arc whose length is 1/2 pie ?

Accepted Solution

Formula to find the arc length is:[tex] s=\frac{\theta}{360} 2\pi r [/tex]So, if we want to measure the central angle then it will be:[tex] \theta= \frac{360s}{2r\pi} [/tex]Where, s= arc length,r = radius of the circle[tex] \theta [/tex]= central angle in degrees.According to the given problem, [tex] s=\frac{1}{2} \pi [/tex] and r = 2.So, first step is to plug in these values in the above formula.[tex] \theta=\frac{360*\frac{1}{2}\pi}{2*2\pi} [/tex][tex] =\frac{360*\frac{1}{2}}{2*2} [/tex] Ο€ has been cancel out from both top and bottom.[tex] =\frac{180}{4} [/tex]=45So, measure of central angle is 45Β°.