Solve sin18.5/x=sin62.5/frac{125{3}}

$$\frac { \sin 18.5 } { x } = \frac { \sin 62.5 } { \frac { 125 } { 3 } }$$

Solve for x

$$x = \frac{132210273502121725}{8870108331782216} = 14\frac{8028756857170704}{8870108331782216} \approx 14.905147554$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.31730465640509214}{x} = \frac{0.8870108331782216}{\frac{125}{3}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$0.31730465640509214=x\times \frac{0.8870108331782216}{\frac{125}{3}}$$

Divide 0.8870108331782216 by \frac{125}{3} by multiplying 0.8870108331782216 by the reciprocal of \frac{125}{3}.

$$0.31730465640509214=x\times 0.8870108331782216\times \frac{3}{125}$$

Convert decimal number 0.8870108331782216 to fraction \frac{1108763541472777}{10000000000}. Reduce the fraction \frac{1108763541472777}{10000000000} to lowest terms by extracting and canceling out 1.

$$0.31730465640509214=x\times \frac{1108763541472777}{1250000000000000}\times \frac{3}{125}$$

Multiply \frac{1108763541472777}{1250000000000000} times \frac{3}{125} by multiplying numerator times numerator and denominator times denominator.

$$0.31730465640509214=x\times \frac{1108763541472777\times 3}{1250000000000000\times 125}$$

Do the multiplications in the fraction \frac{1108763541472777\times 3}{1250000000000000\times 125}.

$$0.31730465640509214=x\times \frac{3326290624418331}{156250000000000000}$$

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

$$x\times \frac{3326290624418331}{156250000000000000}=0.31730465640509214$$

Multiply both sides by \frac{156250000000000000}{3326290624418331}, the reciprocal of \frac{3326290624418331}{156250000000000000}.

$$x=0.31730465640509214\times \frac{156250000000000000}{3326290624418331}$$

Convert decimal number 0.31730465640509214 to fraction \frac{15865232820254607}{10000000000}. Reduce the fraction \frac{15865232820254607}{10000000000} to lowest terms by extracting and canceling out 1.

$$x=\frac{15865232820254607}{50000000000000000}\times \frac{156250000000000000}{3326290624418331}$$

Multiply \frac{15865232820254607}{50000000000000000} times \frac{156250000000000000}{3326290624418331} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{15865232820254607\times 156250000000000000}{50000000000000000\times 3326290624418331}$$

Do the multiplications in the fraction \frac{15865232820254607\times 156250000000000000}{50000000000000000\times 3326290624418331}.

$$x=\frac{2478942628164782343750000000000000}{166314531220916550000000000000000}$$

Reduce the fraction \frac{2478942628164782343750000000000000}{166314531220916550000000000000000} to lowest terms by extracting and canceling out 18750000000000000.

$$x=\frac{132210273502121725}{8870108331782216}$$