Solve sin101/a=sin31/34

$$\frac { \sin 101 } { a } = \frac { \sin 31 } { 34 }$$

Solve for a

$$a = \frac{166876621186102880}{2575190374550271} = 64\frac{2064437214885536}{2575190374550271} \approx 64.801663922$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.981627183447664}{a} = \frac{0.5150380749100542}{34}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 34a, the least common multiple of a,34.

$$34\times 0.981627183447664=a\times 0.5150380749100542$$

Multiply 34 and 0.981627183447664 to get 33.375324237220576.

$$33.375324237220576=a\times 0.5150380749100542$$

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

$$a\times 0.5150380749100542=33.375324237220576$$

Divide both sides by 0.5150380749100542.

$$a=\frac{33.375324237220576}{0.5150380749100542}$$

Expand \frac{33.375324237220576}{0.5150380749100542} by multiplying both numerator and the denominator by 10000000000000000.

$$a=\frac{333753242372205760}{5150380749100542}$$

Reduce the fraction \frac{333753242372205760}{5150380749100542} to lowest terms by extracting and canceling out 2.

$$a=\frac{166876621186102880}{2575190374550271}$$