Solve (16*9.8*sin38^circ)+(0.46*16*9.8*cos38^circ)-89/16

$$\frac { ( 16 \times 9.8 \times \sin 38 ^ { \circ } ) + ( 0.46 \times 16 \times 9.8 \times \cos 38 ^ { \circ } ) - 89 } { 16 }$$

Evaluate

$$4.023334935450553136$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{{(16 \cdot 9.8 \cdot 0.6156614753256582)} + {(0.46 \cdot 16 \cdot 9.8 \cdot 0.788010753606722)} - 89}{16}$$

Multiply 16 and 9.8 to get 156.8.

$$\frac{156.8\times 0.6156614753256582+0.46\times 16\times 9.8\times 0.788010753606722-89}{16}$$

Multiply 156.8 and 0.6156614753256582 to get 96.53571933106320576.

$$\frac{96.53571933106320576+0.46\times 16\times 9.8\times 0.788010753606722-89}{16}$$

Multiply 0.46 and 16 to get 7.36.

$$\frac{96.53571933106320576+7.36\times 9.8\times 0.788010753606722-89}{16}$$

Multiply 7.36 and 9.8 to get 72.128.

$$\frac{96.53571933106320576+72.128\times 0.788010753606722-89}{16}$$

Multiply 72.128 and 0.788010753606722 to get 56.837639636145644416.

$$\frac{96.53571933106320576+56.837639636145644416-89}{16}$$

Add 96.53571933106320576 and 56.837639636145644416 to get 153.373358967208850176.

$$\frac{153.373358967208850176-89}{16}$$

Subtract 89 from 153.373358967208850176 to get 64.373358967208850176.

$$\frac{64.373358967208850176}{16}$$

Expand \frac{64.373358967208850176}{16} by multiplying both numerator and the denominator by 1000000000000000000.

$$\frac{64373358967208850176}{16000000000000000000}$$

Reduce the fraction \frac{64373358967208850176}{16000000000000000000} to lowest terms by extracting and canceling out 256.

$$\frac{251458433465659571}{62500000000000000}$$

Factor

$$\frac{179 \cdot 47143 \cdot 83437 \cdot 357139}{2 ^ {14} \cdot 5 ^ {18}} = 4\frac{1458433465659584}{62500000000000000} = 4.023334935450554$$