Solve sin64^circ/39=sin26^circ/a

$$\frac { \sin 64 ^ { \circ } } { 39 } = \frac { \sin 26 ^ { \circ } } { a }$$

Solve for a

$$a = \frac{85482373623870093}{4493970231495835} = 19\frac{96939225449231}{4493970231495835} \approx 19.021570954$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.898794046299167}{39} = \frac{0.4383711467890774}{a}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 39a, the least common multiple of 39,a.

$$a\times 0.898794046299167=39\times 0.4383711467890774$$

Multiply 39 and 0.4383711467890774 to get 17.0964747247740186.

$$a\times 0.898794046299167=17.0964747247740186$$

Divide both sides by 0.898794046299167.

$$a=\frac{17.0964747247740186}{0.898794046299167}$$

Expand \frac{17.0964747247740186}{0.898794046299167} by multiplying both numerator and the denominator by 10000000000000000.

$$a=\frac{170964747247740186}{8987940462991670}$$

Reduce the fraction \frac{170964747247740186}{8987940462991670} to lowest terms by extracting and canceling out 2.

$$a=\frac{85482373623870093}{4493970231495835}$$