Solve sin101/a=sin31/39

$$\frac { \sin 101 } { a } = \frac { \sin 31 } { 39 }$$

Solve for a

$$a = \frac{63805766924098160}{858396791516757} = 74\frac{284404351858142}{858396791516757} \approx 74.331320381$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.981627183447664}{a} = \frac{0.5150380749100542}{39}$$

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 a,39.

$$39\times 0.981627183447664=a\times 0.5150380749100542$$

Multiply 39 and 0.981627183447664 to get 38.283460154458896.

$$38.283460154458896=a\times 0.5150380749100542$$

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

$$a\times 0.5150380749100542=38.283460154458896$$

Divide both sides by 0.5150380749100542.

$$a=\frac{38.283460154458896}{0.5150380749100542}$$

Expand \frac{38.283460154458896}{0.5150380749100542} by multiplying both numerator and the denominator by 10000000000000000.

$$a=\frac{382834601544588960}{5150380749100542}$$

Reduce the fraction \frac{382834601544588960}{5150380749100542} to lowest terms by extracting and canceling out 6.

$$a=\frac{63805766924098160}{858396791516757}$$