Question

express the centesimal measure as radian measure and sexagesimal measure of (200/9)^g​

Answer 1

Given:-

Express the centesimal measure as radian measure and sexagesimal measure $\sf\large\ { \frac{200}{9} }^{g}$

Solution:-

$\sf\large\ ⇒G \: = \: \frac{200}{9}$

$⇒\sf\large \: \frac{D}{90} \: = \: \frac{G}{100} \: = \: \frac{2c}{\pi}$

$⇒\sf\large\ \frac{D}{90} \: = \: \frac{2 \cancel0 \cancel0}{1 \cancel0 \cancel0} \: = \: \frac{2c}{\pi}$

$\sf\large\ ⇒ \frac{D} {\cancel9 \cancel0} \: = \: \frac{2}{ \cancel9}$

$\sf\large\ ⇒ \: \frac{D}{10} \: = \: \frac{2}{1}$

$\sf\large\ ⇒ \: D \: = \: 2 \: \times \: 10$

$\sf\large\ ⇒ \: D \: = \: 20$

$\sf\ \: {\boxed{\sf{ {( \frac{200}{9} )}^{g} \: = \: 20 \degree}}}$

$\small$

$\sf\large\ ⇒ \frac{ \cancel2}{9} \: = \: \frac{ \cancel2c}{ \pi}$

$\sf\large\ ⇒ \frac{1}{9} \: = \: \frac{c}{ \pi}$

$\sf\large\ ⇒ \: 9c \: = \: \pi$

$\sf\large\ ⇒ \: C \: = \: \frac{ \pi}{9}$

$\sf\large\ ⇒ \: C \: = \: \frac{2 \pi}{2}$

$\sf\ \: {\boxed{\sf{ \therefore \: \frac{200}{9}^{g} \: = \: \frac{2 \pi}{2}}}}$

$\small$

Hence, Solved!