Question

Length of line segment in circle when arc length and radius is given

Answer 1

theta =1 radian

in the triangle with two sides each r uts.

third side c

${c}^{2} = {a}^{2} + {b}^{2} - 2abcosc$

${c}^{2} = {r}^{2} + {r}^{2} - 2 {r}^{2} cos1$

${c}^{2} = 2 {r}^{2} (1 - cos1)$

$= 2 {r}^{2} (2sin { \frac{1}{2} }^{2} )$

$c = 2rsin( \frac{1}{2)}$

which is the length of the line segment