Solve 0.9122+(0.807/0.9122*1.8288*sin60^circ*2.4384)

$$0.9122 + ( \frac { 0.807 } { 0.9122 \times 1.8288 \times \sin 60 ^ { \circ } \times 2.4384 } )$$

Evaluate

$$\frac{3440108388945685630343819}{1928149954994174117895000}\approx 1.784149817$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9122 + {(\frac{0.807}{0.9122 \cdot 1.8288 \cdot 0.5547863447412975})}$$

Multiply 0.9122 and 1.8288 to get 1.66823136.

$$0.9122+\frac{0.807}{1.66823136\times 0.5547863447412975}$$

Multiply 1.66823136 and 0.5547863447412975 to get 0.9255119783972035765896.

$$0.9122+\frac{0.807}{0.9255119783972035765896}$$

Expand \frac{0.807}{0.9255119783972035765896} by multiplying both numerator and the denominator by 10000000000000000000000.

$$0.9122+\frac{8070000000000000000000}{9255119783972035765896}$$

Reduce the fraction \frac{8070000000000000000000}{9255119783972035765896} to lowest terms by extracting and canceling out 24.

$$0.9122+\frac{336250000000000000000}{385629990998834823579}$$

Convert decimal number 0.9122 to fraction \frac{9122}{10000}. Reduce the fraction \frac{9122}{10000} to lowest terms by extracting and canceling out 2.

$$\frac{4561}{5000}+\frac{336250000000000000000}{385629990998834823579}$$

Least common multiple of 5000 and 385629990998834823579 is 1928149954994174117895000. Convert \frac{4561}{5000} and \frac{336250000000000000000}{385629990998834823579} to fractions with denominator 1928149954994174117895000.

$$\frac{1758858388945685630343819}{1928149954994174117895000}+\frac{1681250000000000000000000}{1928149954994174117895000}$$

Since \frac{1758858388945685630343819}{1928149954994174117895000} and \frac{1681250000000000000000000}{1928149954994174117895000} have the same denominator, add them by adding their numerators.

$$\frac{1758858388945685630343819+1681250000000000000000000}{1928149954994174117895000}$$

Add 1758858388945685630343819 and 1681250000000000000000000 to get 3440108388945685630343819.

$$\frac{3440108388945685630343819}{1928149954994174117895000}$$

Factor

$$\frac{11 \cdot 6279359903 \cdot 49803981790943}{13 \cdot 127 \cdot 181 \cdot 4561 \cdot 10479035647 \cdot 2 ^ {3} \cdot 3 ^ {3} \cdot 5 ^ {4}} = 1\frac{1.5119584339515113 \times 10^{24}}{1.9281499549941743 \times 10^{24}} = 1.7841498167895762$$