Solve sin64^circ/3.9=sin26^circ/a

$$\frac { \sin 64 ^ { \circ } } { 3.9 } = \frac { \sin 26 ^ { \circ } } { a }$$

Solve for a

$$a = \frac{85482373623870093}{44939702314958350} = 1\frac{40542671308911740}{44939702314958350} \approx 1.902157095$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.898794046299167}{3.9} = \frac{0.4383711467890774}{a}$$

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

$$a\times \frac{0.898794046299167}{3.9}=0.4383711467890774$$

Expand \frac{0.898794046299167}{3.9} by multiplying both numerator and the denominator by 1000000000000000.

$$a\times \frac{898794046299167}{3900000000000000}=0.4383711467890774$$

Multiply both sides by \frac{3900000000000000}{898794046299167}, the reciprocal of \frac{898794046299167}{3900000000000000}.

$$a=0.4383711467890774\times \frac{3900000000000000}{898794046299167}$$

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.

$$a=\frac{2191855733945387}{5000000000000000}\times \frac{3900000000000000}{898794046299167}$$

Multiply \frac{2191855733945387}{5000000000000000} times \frac{3900000000000000}{898794046299167} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{2191855733945387\times 3900000000000000}{5000000000000000\times 898794046299167}$$

Do the multiplications in the fraction \frac{2191855733945387\times 3900000000000000}{5000000000000000\times 898794046299167}.

$$a=\frac{8548237362387009300000000000000}{4493970231495835000000000000000}$$

Reduce the fraction \frac{8548237362387009300000000000000}{4493970231495835000000000000000} to lowest terms by extracting and canceling out 100000000000000.

$$a=\frac{85482373623870093}{44939702314958350}$$