A sector has an angle of 107.9 and an arc length of 5.92m. Find its radius
A sector has an angle of 107.9 and an arc length of 5.92m. Find its radius
arc length b = 5.92 m
angle $$\alpha \ensurement{^{\circ}}$$ = $$107.9\ensurement{^{\circ}}$$
radius r = ?
$$\boxed{b =r* \breve \alpha} \qquad \breve \alpha =\alpha \ensurement{^{\circ}} * \frac{2\pi}{360\ensurement{^{\circ}}} = \alpha \ensurement{^{\circ}} *\frac{\pi}{180\ensurement{^{\circ}}} \\\\
\begin{array}{rcl}
b &=& r* \breve \alpha \\
&=& r * \alpha \ensurement{^{\circ}} *\frac{\pi}{180\ensurement{^{\circ}}}
\end{array}\\\\\\
\boxed{r = \left( \frac{180\ensurement{^{\circ}} }{\pi} \right)*\frac{b} {\alpha\ensurement{^{\circ}}} = 57.2957795131*\frac{b} {\alpha\ensurement{^{\circ}}} }\\\\
\small{\text{
$
r = \left( \frac{180\ensurement{^{\circ}} }{\pi} \right)*\frac{5.92\ m}{107.9\ensurement{^{\circ}}} = 57.2957795131 * \frac{5.92\ m}{107.9\ensurement{^{\circ}}} = 3.14356825503\ m
$
}}$$
Radius is 3.14356825503 m
A sector has an angle of 107.9 and an arc length of 5.92m. Find its radius
There are 360 degrees in a circle so we hve 107.9/360 of the circle here.
$$\\P=\frac{ 107.9}{360} *2\pi *r\\\\
5.92=\frac{ 107.9}{360} *2\pi *r\\\\
r=\frac{5.92*360}{(107.9*2*\pi)}\\\\$$
A sector has an angle of 107.9 and an arc length of 5.92m. Find its radius
Let us convert 107.9 degrees to radians = 107.9 x pi / 180 = about 1.883 rads
And using S = rΘ where S= the arc length and Θ is in radians, we have
5.92m = r (1.883) divide both sides by (1.883)
r = about 3.144m
A sector has an angle of 107.9 and an arc length of 5.92m. Find its radius
arc length b = 5.92 m
angle $$\alpha \ensurement{^{\circ}}$$ = $$107.9\ensurement{^{\circ}}$$
radius r = ?
$$\boxed{b =r* \breve \alpha} \qquad \breve \alpha =\alpha \ensurement{^{\circ}} * \frac{2\pi}{360\ensurement{^{\circ}}} = \alpha \ensurement{^{\circ}} *\frac{\pi}{180\ensurement{^{\circ}}} \\\\
\begin{array}{rcl}
b &=& r* \breve \alpha \\
&=& r * \alpha \ensurement{^{\circ}} *\frac{\pi}{180\ensurement{^{\circ}}}
\end{array}\\\\\\
\boxed{r = \left( \frac{180\ensurement{^{\circ}} }{\pi} \right)*\frac{b} {\alpha\ensurement{^{\circ}}} = 57.2957795131*\frac{b} {\alpha\ensurement{^{\circ}}} }\\\\
\small{\text{
$
r = \left( \frac{180\ensurement{^{\circ}} }{\pi} \right)*\frac{5.92\ m}{107.9\ensurement{^{\circ}}} = 57.2957795131 * \frac{5.92\ m}{107.9\ensurement{^{\circ}}} = 3.14356825503\ m
$
}}$$
Radius is 3.14356825503 m
My answer and Melody's are approximately the same - depending on the level of rounding. She has taken a "ratio" approach, while I have have used a "trig" approach.......same dog, different fleas....
And heureka has provided a very nice LaTex answer....utilizing a combination of both things....!!!