Solve 50/sin(75^circ)=x/sin(37^circ)

$$\frac{ 50 }{ \sin ( 75 ^ { \circ } ) } = \frac{ x }{ \sin ( 37 ^ { \circ } ) }$$

Solve for x

$$x = \frac{300907511576024150}{9659258262890683} = 31\frac{1470505426412924}{9659258262890684} \approx 31.152237924$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{50}{0.9659258262890683} = \frac{x}{0.6018150231520483}$$

Expand \frac{50}{0.9659258262890683} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{500000000000000000}{9659258262890683}=\frac{x}{0.6018150231520483}$$

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

$$\frac{x}{0.6018150231520483}=\frac{500000000000000000}{9659258262890683}$$

Multiply both sides by 0.6018150231520483.

$$x=\frac{500000000000000000}{9659258262890683}\times 0.6018150231520483$$

Convert decimal number 0.6018150231520483 to fraction \frac{6018150231520483}{10000000000}. Reduce the fraction \frac{6018150231520483}{10000000000} to lowest terms by extracting and canceling out 1.

$$x=\frac{500000000000000000}{9659258262890683}\times \frac{6018150231520483}{10000000000000000}$$

Multiply \frac{500000000000000000}{9659258262890683} times \frac{6018150231520483}{10000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{500000000000000000\times 6018150231520483}{9659258262890683\times 10000000000000000}$$

Do the multiplications in the fraction \frac{500000000000000000\times 6018150231520483}{9659258262890683\times 10000000000000000}.

$$x=\frac{3009075115760241500000000000000000}{96592582628906830000000000000000}$$

Reduce the fraction \frac{3009075115760241500000000000000000}{96592582628906830000000000000000} to lowest terms by extracting and canceling out 10000000000000000.

$$x=\frac{300907511576024150}{9659258262890683}$$