Solve 3eta/sin25^circ=C/sin100^circ

$$\frac { 3 \eta } { \sin 25 ^ { \circ } } = \frac { C } { \sin 100 ^ { \circ } }$$

Solve for C

$$C=\frac{12310096912652600\eta }{1760909423919581}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{3 \eta}{0.42261826174069944} = \frac{C}{0.984807753012208}$$

Divide 3\eta by 0.42261826174069944 to get \frac{12500000000000000}{1760909423919581}\eta .

$$\frac{12500000000000000}{1760909423919581}\eta =\frac{C}{0.984807753012208}$$

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

$$\frac{C}{0.984807753012208}=\frac{12500000000000000}{1760909423919581}\eta$$

The equation is in standard form.

$$\frac{62500000000000}{61550484563263}C=\frac{12500000000000000\eta }{1760909423919581}$$

Divide both sides of the equation by \frac{62500000000000}{61550484563263}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{62500000000000}{61550484563263}C}{\frac{62500000000000}{61550484563263}}=\frac{12500000000000000\eta }{\frac{62500000000000}{61550484563263}\times 1760909423919581}$$

Dividing by \frac{62500000000000}{61550484563263} undoes the multiplication by \frac{62500000000000}{61550484563263}.

$$C=\frac{12500000000000000\eta }{\frac{62500000000000}{61550484563263}\times 1760909423919581}$$

Divide \frac{12500000000000000\eta }{1760909423919581} by \frac{62500000000000}{61550484563263} by multiplying \frac{12500000000000000\eta }{1760909423919581} by the reciprocal of \frac{62500000000000}{61550484563263}.

$$C=\frac{12310096912652600\eta }{1760909423919581}$$

Solve for η

$$\eta =\frac{1760909423919581C}{12310096912652600}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{3 \eta}{0.42261826174069944} = \frac{C}{0.984807753012208}$$

Divide 3\eta by 0.42261826174069944 to get \frac{12500000000000000}{1760909423919581}\eta .

$$\frac{12500000000000000}{1760909423919581}\eta =\frac{C}{0.984807753012208}$$

The equation is in standard form.

$$\frac{12500000000000000}{1760909423919581}\eta =\frac{62500000000000C}{61550484563263}$$

Divide both sides of the equation by \frac{12500000000000000}{1760909423919581}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{12500000000000000}{1760909423919581}\eta }{\frac{12500000000000000}{1760909423919581}}=\frac{62500000000000C}{\frac{12500000000000000}{1760909423919581}\times 61550484563263}$$

Dividing by \frac{12500000000000000}{1760909423919581} undoes the multiplication by \frac{12500000000000000}{1760909423919581}.

$$\eta =\frac{62500000000000C}{\frac{12500000000000000}{1760909423919581}\times 61550484563263}$$

Divide \frac{62500000000000C}{61550484563263} by \frac{12500000000000000}{1760909423919581} by multiplying \frac{62500000000000C}{61550484563263} by the reciprocal of \frac{12500000000000000}{1760909423919581}.

$$\eta =\frac{1760909423919581C}{12310096912652600}$$