Whakaoti i te gamma^2=operatorname{arcos}(55^2+76^2+93812/2(55)(76)

$$\gamma ^ { 2 } = \operatorname { arcos } ( \frac { 55 ^ { 2 } + 76 ^ { 2 } + 93812 } { 2 ( 55 ) ( 76 ) }$$

Whakaoti mō a

$$\left\{\begin{matrix}a=\frac{\gamma ^{2}}{\cos(\frac{102613}{8360})r}\text{, }&r\neq 0\\a\in \mathrm{R}\text{, }&\gamma =0\text{ and }r=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 55 mā te pū o 2, kia riro ko 3025.

$$\gamma ^{2}=ar\cos(\frac{3025+76^{2}+93812}{2\times 55\times 76})$$

Tātaihia te 76 mā te pū o 2, kia riro ko 5776.

$$\gamma ^{2}=ar\cos(\frac{3025+5776+93812}{2\times 55\times 76})$$

Tāpirihia te 3025 ki te 5776, ka 8801.

$$\gamma ^{2}=ar\cos(\frac{8801+93812}{2\times 55\times 76})$$

Tāpirihia te 8801 ki te 93812, ka 102613.

$$\gamma ^{2}=ar\cos(\frac{102613}{2\times 55\times 76})$$

Whakareatia te 2 ki te 55, ka 110.

$$\gamma ^{2}=ar\cos(\frac{102613}{110\times 76})$$

Whakareatia te 110 ki te 76, ka 8360.

$$\gamma ^{2}=ar\cos(\frac{102613}{8360})$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ar\cos(\frac{102613}{8360})=\gamma ^{2}$$

He hanga arowhānui tō te whārite.

$$\cos(\frac{102613}{8360})ra=\gamma ^{2}$$

Whakawehea ngā taha e rua ki te r\cos(\frac{102613}{8360}).

$$\frac{\cos(\frac{102613}{8360})ra}{\cos(\frac{102613}{8360})r}=\frac{\gamma ^{2}}{\cos(\frac{102613}{8360})r}$$

Mā te whakawehe ki te r\cos(\frac{102613}{8360}) ka wetekia te whakareanga ki te r\cos(\frac{102613}{8360}).

$$a=\frac{\gamma ^{2}}{\cos(\frac{102613}{8360})r}$$

Whakaoti mō r

$$\left\{\begin{matrix}r=\frac{\gamma ^{2}}{\cos(\frac{102613}{8360})a}\text{, }&a\neq 0\\r\in \mathrm{R}\text{, }&\gamma =0\text{ and }a=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 55 mā te pū o 2, kia riro ko 3025.

$$\gamma ^{2}=ar\cos(\frac{3025+76^{2}+93812}{2\times 55\times 76})$$

Tātaihia te 76 mā te pū o 2, kia riro ko 5776.

$$\gamma ^{2}=ar\cos(\frac{3025+5776+93812}{2\times 55\times 76})$$

Tāpirihia te 3025 ki te 5776, ka 8801.

$$\gamma ^{2}=ar\cos(\frac{8801+93812}{2\times 55\times 76})$$

Tāpirihia te 8801 ki te 93812, ka 102613.

$$\gamma ^{2}=ar\cos(\frac{102613}{2\times 55\times 76})$$

Whakareatia te 2 ki te 55, ka 110.

$$\gamma ^{2}=ar\cos(\frac{102613}{110\times 76})$$

Whakareatia te 110 ki te 76, ka 8360.

$$\gamma ^{2}=ar\cos(\frac{102613}{8360})$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ar\cos(\frac{102613}{8360})=\gamma ^{2}$$

He hanga arowhānui tō te whārite.

$$\cos(\frac{102613}{8360})ar=\gamma ^{2}$$

Whakawehea ngā taha e rua ki te a\cos(\frac{102613}{8360}).

$$\frac{\cos(\frac{102613}{8360})ar}{\cos(\frac{102613}{8360})a}=\frac{\gamma ^{2}}{\cos(\frac{102613}{8360})a}$$

Mā te whakawehe ki te a\cos(\frac{102613}{8360}) ka wetekia te whakareanga ki te a\cos(\frac{102613}{8360}).

$$r=\frac{\gamma ^{2}}{\cos(\frac{102613}{8360})a}$$