Solve sin5^circ/7=sin40^circ/a

$$\frac { \sin 5 ^ { \circ } } { 7 } = \frac { \sin 40 ^ { \circ } } { a }$$

Solve for a

$$a = \frac{449951326780577510}{8715574274765817} = 51\frac{5457038767520869}{8715574274765817} \approx 51.62612498$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.08715574274765817}{7} = \frac{0.6427876096865393}{a}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7a, the least common multiple of 7,a.

$$a\times 0.08715574274765817=7\times 0.6427876096865393$$

Multiply 7 and 0.6427876096865393 to get 4.4995132678057751.

$$a\times 0.08715574274765817=4.4995132678057751$$

Divide both sides by 0.08715574274765817.

$$a=\frac{4.4995132678057751}{0.08715574274765817}$$

Expand \frac{4.4995132678057751}{0.08715574274765817} by multiplying both numerator and the denominator by 100000000000000000.

$$a=\frac{449951326780577510}{8715574274765817}$$