Solve 120*5280/3600*sin35^circ*3.919-1/2*32.2*3.919^2

$$\frac { 120 \times 5280 } { 3600 } \times \sin 35 ^ { \circ } \times 3.919 - \frac { 1 } { 2 } \times 32.2 \times 3.919 ^ { 2 }$$

Evaluate

$$-127.6122998941598272$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{120 \cdot 5280}{3600} \cdot 0.6798893875331828 - \frac{1}{2} \cdot 32.2 \cdot 3.919 ^ {2}$$

Multiply 120 and 5280 to get 633600.

$$\frac{633600}{3600}\times 0.6798893875331828-\frac{1}{2}\times 32.2\times 3.919^{2}$$

Divide 633600 by 3600 to get 176.

$$176\times 0.6798893875331828-\frac{1}{2}\times 32.2\times 3.919^{2}$$

Multiply 176 and 0.6798893875331828 to get 119.6605322058401728.

$$119.6605322058401728-\frac{1}{2}\times 32.2\times 3.919^{2}$$

Convert decimal number 32.2 to fraction \frac{322}{10}. Reduce the fraction \frac{322}{10} to lowest terms by extracting and canceling out 2.

$$119.6605322058401728-\frac{1}{2}\times \frac{161}{5}\times 3.919^{2}$$

Multiply \frac{1}{2} times \frac{161}{5} by multiplying numerator times numerator and denominator times denominator.

$$119.6605322058401728-\frac{1\times 161}{2\times 5}\times 3.919^{2}$$

Do the multiplications in the fraction \frac{1\times 161}{2\times 5}.

$$119.6605322058401728-\frac{161}{10}\times 3.919^{2}$$

Calculate 3.919 to the power of 2 and get 15.358561.

$$119.6605322058401728-\frac{161}{10}\times 15.358561$$

Convert decimal number 15.358561 to fraction \frac{15358561}{1000000}.

$$119.6605322058401728-\frac{161}{10}\times \frac{15358561}{1000000}$$

Multiply \frac{161}{10} times \frac{15358561}{1000000} by multiplying numerator times numerator and denominator times denominator.

$$119.6605322058401728-\frac{161\times 15358561}{10\times 1000000}$$

Do the multiplications in the fraction \frac{161\times 15358561}{10\times 1000000}.

$$119.6605322058401728-\frac{2472728321}{10000000}$$

Convert decimal number 119.6605322058401728 to fraction \frac{18696958157162527}{10000000000}. Reduce the fraction \frac{18696958157162527}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{18696958157162527}{156250000000000}-\frac{2472728321}{10000000}$$

Least common multiple of 156250000000000 and 10000000 is 156250000000000. Convert \frac{18696958157162527}{156250000000000} and \frac{2472728321}{10000000} to fractions with denominator 156250000000000.

$$\frac{18696958157162527}{156250000000000}-\frac{38636380015625000}{156250000000000}$$

Since \frac{18696958157162527}{156250000000000} and \frac{38636380015625000}{156250000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18696958157162527-38636380015625000}{156250000000000}$$

Subtract 38636380015625000 from 18696958157162527 to get -19939421858462473.

$$-\frac{19939421858462473}{156250000000000}$$

Factor

$$-127.6122998941598272$$