Solve 1.4/(frac{1{53457}+1/53457)sin40^circ}

$$\frac { 1.4 } { ( \frac { 1 } { 53457 } + \frac { 1 } { 53457 } ) \sin 40 ^ { \circ } }$$

Evaluate

$$\frac{374199000000000000000}{6427876096865393}\approx 58215.030028734$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1.4}{{(\frac{1}{53457} + \frac{1}{53457})} 0.6427876096865393}$$

Since \frac{1}{53457} and \frac{1}{53457} have the same denominator, add them by adding their numerators.

$$\frac{1.4}{\frac{1+1}{53457}\times 0.6427876096865393}$$

Add 1 and 1 to get 2.

$$\frac{1.4}{\frac{2}{53457}\times 0.6427876096865393}$$

Convert decimal number 0.6427876096865393 to fraction \frac{6427876096865393}{10000000000}. Reduce the fraction \frac{6427876096865393}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1.4}{\frac{2}{53457}\times \frac{6427876096865393}{10000000000000000}}$$

Multiply \frac{2}{53457} times \frac{6427876096865393}{10000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1.4}{\frac{2\times 6427876096865393}{53457\times 10000000000000000}}$$

Do the multiplications in the fraction \frac{2\times 6427876096865393}{53457\times 10000000000000000}.

$$\frac{1.4}{\frac{12855752193730786}{534570000000000000000}}$$

Reduce the fraction \frac{12855752193730786}{534570000000000000000} to lowest terms by extracting and canceling out 2.

$$\frac{1.4}{\frac{6427876096865393}{267285000000000000000}}$$

Divide 1.4 by \frac{6427876096865393}{267285000000000000000} by multiplying 1.4 by the reciprocal of \frac{6427876096865393}{267285000000000000000}.

$$1.4\times \frac{267285000000000000000}{6427876096865393}$$

Convert decimal number 1.4 to fraction \frac{14}{10}. Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$\frac{7}{5}\times \frac{267285000000000000000}{6427876096865393}$$

Multiply \frac{7}{5} times \frac{267285000000000000000}{6427876096865393} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 267285000000000000000}{5\times 6427876096865393}$$

Do the multiplications in the fraction \frac{7\times 267285000000000000000}{5\times 6427876096865393}.

$$\frac{1870995000000000000000}{32139380484326965}$$

Reduce the fraction \frac{1870995000000000000000}{32139380484326965} to lowest terms by extracting and canceling out 5.

$$\frac{374199000000000000000}{6427876096865393}$$

Factor

$$\frac{3 \cdot 7 \cdot 103 \cdot 173 \cdot 2 ^ {15} \cdot 5 ^ {15}}{6427876096865393} = 58215\frac{193020981179273}{6427876096865393} = 58215.03002873395$$