Solve 1/2*9.81t-20cos15^circ/20sin15^circ=tan15^circ

$$\frac { \frac { 1 } { 2 } \times 9.81 t - 20 \cos 15 ^ { \circ } } { 20 \sin 15 ^ { \circ } } = \tan 15 ^ { \circ }$$

Solve for t

$$t = \frac{517638090205041527491131299117399}{122625000000000000000000000000000} = 4\frac{2.713809020504151 \times 10^{31}}{1.2262499999999998 \times 10^{32}} \approx 4.221309604$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{\frac{1}{2} \cdot 9.81 t - 20 \cdot 0.9659258262890683}{20 \cdot 0.25881904510252074} = 0.2679491924311227$$

Convert decimal number 9.81 to fraction \frac{981}{100}.

$$\frac{\frac{1}{2}\times \frac{981}{100}t-20\times 0.9659258262890683}{20\times 0.25881904510252074}=0.2679491924311227$$

Multiply \frac{1}{2} times \frac{981}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 981}{2\times 100}t-20\times 0.9659258262890683}{20\times 0.25881904510252074}=0.2679491924311227$$

Do the multiplications in the fraction \frac{1\times 981}{2\times 100}.

$$\frac{\frac{981}{200}t-20\times 0.9659258262890683}{20\times 0.25881904510252074}=0.2679491924311227$$

Multiply 20 and 0.9659258262890683 to get 19.318516525781366.

$$\frac{\frac{981}{200}t-19.318516525781366}{20\times 0.25881904510252074}=0.2679491924311227$$

Multiply 20 and 0.25881904510252074 to get 5.1763809020504148.

$$\frac{\frac{981}{200}t-19.318516525781366}{5.1763809020504148}=0.2679491924311227$$

Divide each term of \frac{981}{200}t-19.318516525781366 by 5.1763809020504148 to get \frac{\frac{981}{200}t}{5.1763809020504148}+\frac{-19.318516525781366}{5.1763809020504148}.

$$\frac{\frac{981}{200}t}{5.1763809020504148}+\frac{-19.318516525781366}{5.1763809020504148}=0.2679491924311227$$

Divide \frac{981}{200}t by 5.1763809020504148 to get \frac{1362500000000000}{1437883583902893}t.

$$\frac{1362500000000000}{1437883583902893}t+\frac{-19.318516525781366}{5.1763809020504148}=0.2679491924311227$$

Expand \frac{-19.318516525781366}{5.1763809020504148} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{1362500000000000}{1437883583902893}t+\frac{-193185165257813660}{51763809020504148}=0.2679491924311227$$

Reduce the fraction \frac{-193185165257813660}{51763809020504148} to lowest terms by extracting and canceling out 4.

$$\frac{1362500000000000}{1437883583902893}t-\frac{48296291314453415}{12940952255126037}=0.2679491924311227$$

Add \frac{48296291314453415}{12940952255126037} to both sides.

$$\frac{1362500000000000}{1437883583902893}t=0.2679491924311227+\frac{48296291314453415}{12940952255126037}$$

Convert decimal number 0.2679491924311227 to fraction \frac{2679491924311227}{10000000000}. Reduce the fraction \frac{2679491924311227}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1362500000000000}{1437883583902893}t=\frac{2679491924311227}{10000000000000000}+\frac{48296291314453415}{12940952255126037}$$

Least common multiple of 10000000000000000 and 12940952255126037 is 129409522551260370000000000000000. Convert \frac{2679491924311227}{10000000000000000} and \frac{48296291314453415}{12940952255126037} to fractions with denominator 129409522551260370000000000000000.

$$\frac{1362500000000000}{1437883583902893}t=\frac{34675177060507377491131299117399}{129409522551260370000000000000000}+\frac{482962913144534150000000000000000}{129409522551260370000000000000000}$$

Since \frac{34675177060507377491131299117399}{129409522551260370000000000000000} and \frac{482962913144534150000000000000000}{129409522551260370000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{1362500000000000}{1437883583902893}t=\frac{34675177060507377491131299117399+482962913144534150000000000000000}{129409522551260370000000000000000}$$

Add 34675177060507377491131299117399 and 482962913144534150000000000000000 to get 517638090205041527491131299117399.

$$\frac{1362500000000000}{1437883583902893}t=\frac{517638090205041527491131299117399}{129409522551260370000000000000000}$$

Multiply both sides by \frac{1437883583902893}{1362500000000000}, the reciprocal of \frac{1362500000000000}{1437883583902893}.

$$t=\frac{517638090205041527491131299117399}{129409522551260370000000000000000}\times \frac{1437883583902893}{1362500000000000}$$

Multiply \frac{517638090205041527491131299117399}{129409522551260370000000000000000} times \frac{1437883583902893}{1362500000000000} by multiplying numerator times numerator and denominator times denominator.

$$t=\frac{517638090205041527491131299117399\times 1437883583902893}{129409522551260370000000000000000\times 1362500000000000}$$

Do the multiplications in the fraction \frac{517638090205041527491131299117399\times 1437883583902893}{129409522551260370000000000000000\times 1362500000000000}.

$$t=\frac{744303312308674124392241432979420423814622735307}{176320474476092254125000000000000000000000000000}$$

Reduce the fraction \frac{744303312308674124392241432979420423814622735307}{176320474476092254125000000000000000000000000000} to lowest terms by extracting and canceling out 1437883583902893.

$$t=\frac{517638090205041527491131299117399}{122625000000000000000000000000000}$$