Solve gamma^2=operatorname{arcos}(55^2+76^2+93.812/2(55)(76)

$$\gamma ^ { 2 } = \operatorname { arcos } ( \frac { 55 ^ { 2 } + 76 ^ { 2 } + 93.812 } { 2 ( 55 ) ( 76 ) }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\gamma ^{2}}{\cos(\frac{117037}{110000})r}\text{, }&r\neq 0\\a\in \mathrm{R}\text{, }&\gamma =0\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 55 to the power of 2 and get 3025.

$$\gamma ^{2}=ar\cos(\frac{3025+76^{2}+93.812}{2\times 55\times 76})$$

Calculate 76 to the power of 2 and get 5776.

$$\gamma ^{2}=ar\cos(\frac{3025+5776+93.812}{2\times 55\times 76})$$

Add 3025 and 5776 to get 8801.

$$\gamma ^{2}=ar\cos(\frac{8801+93.812}{2\times 55\times 76})$$

Add 8801 and 93.812 to get 8894.812.

$$\gamma ^{2}=ar\cos(\frac{8894.812}{2\times 55\times 76})$$

Multiply 2 and 55 to get 110.

$$\gamma ^{2}=ar\cos(\frac{8894.812}{110\times 76})$$

Multiply 110 and 76 to get 8360.

$$\gamma ^{2}=ar\cos(\frac{8894.812}{8360})$$

Expand \frac{8894.812}{8360} by multiplying both numerator and the denominator by 1000.

$$\gamma ^{2}=ar\cos(\frac{8894812}{8360000})$$

Reduce the fraction \frac{8894812}{8360000} to lowest terms by extracting and canceling out 76.

$$\gamma ^{2}=ar\cos(\frac{117037}{110000})$$

Swap sides so that all variable terms are on the left hand side.

$$ar\cos(\frac{117037}{110000})=\gamma ^{2}$$

The equation is in standard form.

$$\cos(\frac{117037}{110000})ra=\gamma ^{2}$$

Divide both sides by r\cos(\frac{117037}{110000}).

$$\frac{\cos(\frac{117037}{110000})ra}{\cos(\frac{117037}{110000})r}=\frac{\gamma ^{2}}{\cos(\frac{117037}{110000})r}$$

Dividing by r\cos(\frac{117037}{110000}) undoes the multiplication by r\cos(\frac{117037}{110000}).

$$a=\frac{\gamma ^{2}}{\cos(\frac{117037}{110000})r}$$

Solve for r

$$\left\{\begin{matrix}r=\frac{\gamma ^{2}}{\cos(\frac{117037}{110000})a}\text{, }&a\neq 0\\r\in \mathrm{R}\text{, }&\gamma =0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 55 to the power of 2 and get 3025.

$$\gamma ^{2}=ar\cos(\frac{3025+76^{2}+93.812}{2\times 55\times 76})$$

Calculate 76 to the power of 2 and get 5776.

$$\gamma ^{2}=ar\cos(\frac{3025+5776+93.812}{2\times 55\times 76})$$

Add 3025 and 5776 to get 8801.

$$\gamma ^{2}=ar\cos(\frac{8801+93.812}{2\times 55\times 76})$$

Add 8801 and 93.812 to get 8894.812.

$$\gamma ^{2}=ar\cos(\frac{8894.812}{2\times 55\times 76})$$

Multiply 2 and 55 to get 110.

$$\gamma ^{2}=ar\cos(\frac{8894.812}{110\times 76})$$

Multiply 110 and 76 to get 8360.

$$\gamma ^{2}=ar\cos(\frac{8894.812}{8360})$$

Expand \frac{8894.812}{8360} by multiplying both numerator and the denominator by 1000.

$$\gamma ^{2}=ar\cos(\frac{8894812}{8360000})$$

Reduce the fraction \frac{8894812}{8360000} to lowest terms by extracting and canceling out 76.

$$\gamma ^{2}=ar\cos(\frac{117037}{110000})$$

Swap sides so that all variable terms are on the left hand side.

$$ar\cos(\frac{117037}{110000})=\gamma ^{2}$$

The equation is in standard form.

$$\cos(\frac{117037}{110000})ar=\gamma ^{2}$$

Divide both sides by a\cos(\frac{117037}{110000}).

$$\frac{\cos(\frac{117037}{110000})ar}{\cos(\frac{117037}{110000})a}=\frac{\gamma ^{2}}{\cos(\frac{117037}{110000})a}$$

Dividing by a\cos(\frac{117037}{110000}) undoes the multiplication by a\cos(\frac{117037}{110000}).

$$r=\frac{\gamma ^{2}}{\cos(\frac{117037}{110000})a}$$