Solve sin4.1^circ/a=sin4.6^circ/21

$$\frac { \sin 4.1 ^ { \circ } } { a } = \frac { \sin 4.6 ^ { \circ } } { 21 }$$

Solve for a

$$a = \frac{50048211032880137}{2673297477628630} = 18\frac{1928856435564796}{2673297477628630} \approx 18.721527047$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.07149744433268591}{a} = \frac{0.0801989243288589}{21}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 21a, the least common multiple of a,21.

$$21\times 0.07149744433268591=a\times 0.0801989243288589$$

Multiply 21 and 0.07149744433268591 to get 1.50144633098640411.

$$1.50144633098640411=a\times 0.0801989243288589$$

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

$$a\times 0.0801989243288589=1.50144633098640411$$

Divide both sides by 0.0801989243288589.

$$a=\frac{1.50144633098640411}{0.0801989243288589}$$

Expand \frac{1.50144633098640411}{0.0801989243288589} by multiplying both numerator and the denominator by 100000000000000000.

$$a=\frac{150144633098640411}{8019892432885890}$$

Reduce the fraction \frac{150144633098640411}{8019892432885890} to lowest terms by extracting and canceling out 3.

$$a=\frac{50048211032880137}{2673297477628630}$$