Solve 27/sin(46)*sin(78)

$$\frac{ 27 }{ \sin ( 46 ) } \times \sin ( 78 )$$

Evaluate

$$\frac{37728550314018216}{1027628286198073}\approx 36.714199892$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{27}{0.7193398003386511} \cdot 0.9781476007338056$$

Expand \frac{27}{0.7193398003386511} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{270000000000000000}{7193398003386511}\times 0.9781476007338056$$

Convert decimal number 0.9781476007338056 to fraction \frac{1222684500917257}{10000000000}. Reduce the fraction \frac{1222684500917257}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{270000000000000000}{7193398003386511}\times \frac{1222684500917257}{1250000000000000}$$

Multiply \frac{270000000000000000}{7193398003386511} times \frac{1222684500917257}{1250000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{270000000000000000\times 1222684500917257}{7193398003386511\times 1250000000000000}$$

Do the multiplications in the fraction \frac{270000000000000000\times 1222684500917257}{7193398003386511\times 1250000000000000}.

$$\frac{330124815247659390000000000000000}{8991747504233138750000000000000}$$

Reduce the fraction \frac{330124815247659390000000000000000}{8991747504233138750000000000000} to lowest terms by extracting and canceling out 8750000000000000.

$$\frac{37728550314018216}{1027628286198073}$$

Factor

$$\frac{43891 \cdot 3979613461 \cdot 2 ^ {3} \cdot 3 ^ {3}}{12973 \cdot 1616588749 \cdot 7 ^ {2}} = 36\frac{733932010887588}{1027628286198073} = 36.714199891872305$$