Solve sin(10^circ)/sin(70^circ)sin(80^circ)/sin(20^circ)

$$\frac{ \sin ( 10 ^ { \circ } ) }{ \sin ( 70 ^ { \circ } ) } \frac{ \sin ( 80 ^ { \circ } ) }{ \sin ( 20 ^ { \circ } ) }$$

Evaluate

$$\frac{17101007166283433764780637546864}{32139380484326960336182663438021}\approx 0.532088886$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.17364817766693033}{0.9396926207859083} \frac{0.984807753012208}{0.3420201433256687}$$

Expand \frac{0.17364817766693033}{0.9396926207859083} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{17364817766693033}{93969262078590830}\times \frac{0.984807753012208}{0.3420201433256687}$$

Expand \frac{0.984807753012208}{0.3420201433256687} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{17364817766693033}{93969262078590830}\times \frac{9848077530122080}{3420201433256687}$$

Multiply \frac{17364817766693033}{93969262078590830} times \frac{9848077530122080}{3420201433256687} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17364817766693033\times 9848077530122080}{93969262078590830\times 3420201433256687}$$

Do the multiplications in the fraction \frac{17364817766693033\times 9848077530122080}{93969262078590830\times 3420201433256687}.

$$\frac{171010071662834337647806375468640}{321393804843269603361826634380210}$$

Reduce the fraction \frac{171010071662834337647806375468640}{321393804843269603361826634380210} to lowest terms by extracting and canceling out 10.

$$\frac{17101007166283433764780637546864}{32139380484326960336182663438021}$$

Factor

$$\frac{7 \cdot 13 \cdot 59 \cdot 241 \cdot 443 \cdot 2399 \cdot 57915859 \cdot 13420224577 \cdot 2 ^ {4}}{179 \cdot 25693 \cdot 87553 \cdot 743676121 \cdot 107328432011} = 0.532088886237956$$