Solve sin35^circ/a=sin85^circ/44

$$\frac { \sin 35 ^ { \circ } } { a } = \frac { \sin 85 ^ { \circ } } { 44 }$$

Solve for a

$$a = \frac{50474726398892048}{1992389396183491} = 25\frac{664991494304773}{1992389396183491} \approx 25.333765827$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.573576436351046}{a} = \frac{0.9961946980917455}{44}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 44a, the least common multiple of a,44.

$$44\times 0.573576436351046=a\times 0.9961946980917455$$

Multiply 44 and 0.573576436351046 to get 25.237363199446024.

$$25.237363199446024=a\times 0.9961946980917455$$

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

$$a\times 0.9961946980917455=25.237363199446024$$

Divide both sides by 0.9961946980917455.

$$a=\frac{25.237363199446024}{0.9961946980917455}$$

Expand \frac{25.237363199446024}{0.9961946980917455} by multiplying both numerator and the denominator by 10000000000000000.

$$a=\frac{252373631994460240}{9961946980917455}$$

Reduce the fraction \frac{252373631994460240}{9961946980917455} to lowest terms by extracting and canceling out 5.

$$a=\frac{50474726398892048}{1992389396183491}$$