Solve x=200tan(10)/tan(40)-tan(10)tan(40)

$$x = \frac{ 200 \tan ( 10 ) }{ \tan ( 40 ) - \tan ( 10 ) } \tan ( 40 )$$

Solve for x

$$x = \frac{73977952239538156400860490403951}{1656931626172037300000000000000} = 44\frac{1.0729606879685196 \times 10^{30}}{1.6569316261720373 \times 10^{30}} \approx 44.64755882$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$x = \frac{200 \cdot 0.17632698070846498}{0.8390996311772799 - 0.17632698070846498} 0.8390996311772799$$

Multiply 200 and 0.17632698070846498 to get 35.265396141692996.

$$x=\frac{35.265396141692996}{0.8390996311772799-0.17632698070846498}\times 0.8390996311772799$$

Subtract 0.17632698070846498 from 0.8390996311772799 to get 0.66277265046881492.

$$x=\frac{35.265396141692996}{0.66277265046881492}\times 0.8390996311772799$$

Expand \frac{35.265396141692996}{0.66277265046881492} by multiplying both numerator and the denominator by 100000000000000000.

$$x=\frac{3526539614169299600}{66277265046881492}\times 0.8390996311772799$$

Reduce the fraction \frac{3526539614169299600}{66277265046881492} to lowest terms by extracting and canceling out 4.

$$x=\frac{881634903542324900}{16569316261720373}\times 0.8390996311772799$$

Convert decimal number 0.8390996311772799 to fraction \frac{8390996311772799}{10000000000}. Reduce the fraction \frac{8390996311772799}{10000000000} to lowest terms by extracting and canceling out 1.

$$x=\frac{881634903542324900}{16569316261720373}\times \frac{8390996311772799}{10000000000000000}$$

Multiply \frac{881634903542324900}{16569316261720373} times \frac{8390996311772799}{10000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{881634903542324900\times 8390996311772799}{16569316261720373\times 10000000000000000}$$

Do the multiplications in the fraction \frac{881634903542324900\times 8390996311772799}{16569316261720373\times 10000000000000000}.

$$x=\frac{7397795223953815640086049040395100}{165693162617203730000000000000000}$$

Reduce the fraction \frac{7397795223953815640086049040395100}{165693162617203730000000000000000} to lowest terms by extracting and canceling out 100.

$$x=\frac{73977952239538156400860490403951}{1656931626172037300000000000000}$$

Assign x

$$x≔\frac{73977952239538156400860490403951}{1656931626172037300000000000000}$$