Solve sin52^circ/45=sin118^circ/a

$$\frac { \sin 52 ^ { \circ } } { 45 } = \frac { \sin 118 ^ { \circ } } { a }$$

Solve for a

$$a = \frac{79465283357303439}{1576021507213444} = 50\frac{664207996631240}{1576021507213444} \approx 50.421446023$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.788010753606722}{45} = \frac{0.8829475928589271}{a}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 45a, the least common multiple of 45,a.

$$a\times 0.788010753606722=45\times 0.8829475928589271$$

Multiply 45 and 0.8829475928589271 to get 39.7326416786517195.

$$a\times 0.788010753606722=39.7326416786517195$$

Divide both sides by 0.788010753606722.

$$a=\frac{39.7326416786517195}{0.788010753606722}$$

Expand \frac{39.7326416786517195}{0.788010753606722} by multiplying both numerator and the denominator by 10000000000000000.

$$a=\frac{397326416786517195}{7880107536067220}$$

Reduce the fraction \frac{397326416786517195}{7880107536067220} to lowest terms by extracting and canceling out 5.

$$a=\frac{79465283357303439}{1576021507213444}$$