Solve sin26/a=sin14/3.9

$$\frac { \sin 26 } { a } = \frac { \sin 14 } { 3.9 }$$

Solve for a

$$a = \frac{56988249082580062}{8064063186655591} = 7\frac{539806775990927}{8064063186655591} \approx 7.0669398$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.4383711467890774}{a} = \frac{0.24192189559966773}{3.9}$$

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

$$0.4383711467890774=a\times \frac{0.24192189559966773}{3.9}$$

Expand \frac{0.24192189559966773}{3.9} by multiplying both numerator and the denominator by 100000000000000000.

$$0.4383711467890774=a\times \frac{24192189559966773}{390000000000000000}$$

Reduce the fraction \frac{24192189559966773}{390000000000000000} to lowest terms by extracting and canceling out 3.

$$0.4383711467890774=a\times \frac{8064063186655591}{130000000000000000}$$

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

$$a\times \frac{8064063186655591}{130000000000000000}=0.4383711467890774$$

Multiply both sides by \frac{130000000000000000}{8064063186655591}, the reciprocal of \frac{8064063186655591}{130000000000000000}.

$$a=0.4383711467890774\times \frac{130000000000000000}{8064063186655591}$$

Convert decimal number 0.4383711467890774 to fraction \frac{2191855733945387}{10000000000}. Reduce the fraction \frac{2191855733945387}{10000000000} to lowest terms by extracting and canceling out 1.

$$a=\frac{2191855733945387}{5000000000000000}\times \frac{130000000000000000}{8064063186655591}$$

Multiply \frac{2191855733945387}{5000000000000000} times \frac{130000000000000000}{8064063186655591} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{2191855733945387\times 130000000000000000}{5000000000000000\times 8064063186655591}$$

Do the multiplications in the fraction \frac{2191855733945387\times 130000000000000000}{5000000000000000\times 8064063186655591}.

$$a=\frac{284941245412900310000000000000000}{40320315933277955000000000000000}$$

Reduce the fraction \frac{284941245412900310000000000000000}{40320315933277955000000000000000} to lowest terms by extracting and canceling out 5000000000000000.

$$a=\frac{56988249082580062}{8064063186655591}$$