Solve sin4^circ/3.9=sin26^circ/a

$$\frac { \sin 4 ^ { \circ } } { 3.9 } = \frac { \sin 26 ^ { \circ } } { a }$$

Solve for a

$$a = \frac{85482373623870093}{3487823687206265} = 24\frac{1774605130919736}{3487823687206265} \approx 24.508800126$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.0697564737441253}{3.9} = \frac{0.4383711467890774}{a}$$

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

$$a\times \frac{0.0697564737441253}{3.9}=0.4383711467890774$$

Expand \frac{0.0697564737441253}{3.9} by multiplying both numerator and the denominator by 10000000000000000.

$$a\times \frac{697564737441253}{39000000000000000}=0.4383711467890774$$

Multiply both sides by \frac{39000000000000000}{697564737441253}, the reciprocal of \frac{697564737441253}{39000000000000000}.

$$a=0.4383711467890774\times \frac{39000000000000000}{697564737441253}$$

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.

$$a=\frac{2191855733945387}{5000000000000000}\times \frac{39000000000000000}{697564737441253}$$

Multiply \frac{2191855733945387}{5000000000000000} times \frac{39000000000000000}{697564737441253} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{2191855733945387\times 39000000000000000}{5000000000000000\times 697564737441253}$$

Do the multiplications in the fraction \frac{2191855733945387\times 39000000000000000}{5000000000000000\times 697564737441253}.

$$a=\frac{85482373623870093000000000000000}{3487823687206265000000000000000}$$

Reduce the fraction \frac{85482373623870093000000000000000}{3487823687206265000000000000000} to lowest terms by extracting and canceling out 1000000000000000.

$$a=\frac{85482373623870093}{3487823687206265}$$