Solve 21^2+30^2-(2(21)(30)(cos(123)))

$${ 21 }^{ 2 } + { 30 }^{ 2 } -(2(21)(30)( \cos ( 123) ) )$$

Evaluate

$$2027.245184118934146$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(21)} ^ {2} + {(30)} ^ {2} - {(2 {(21)} {(30)} \cdot -0.5446390350150271)}$$

Calculate 21 to the power of 2 and get 441.

$$441+30^{2}-2\times 21\times 30\left(-0.5446390350150271\right)$$

Calculate 30 to the power of 2 and get 900.

$$441+900-2\times 21\times 30\left(-0.5446390350150271\right)$$

Add 441 and 900 to get 1341.

$$1341-2\times 21\times 30\left(-0.5446390350150271\right)$$

Multiply 2 and 21 to get 42.

$$1341-42\times 30\left(-0.5446390350150271\right)$$

Multiply 42 and 30 to get 1260.

$$1341-1260\left(-0.5446390350150271\right)$$

Multiply 1260 and -0.5446390350150271 to get -686.245184118934146.

$$1341-\left(-686.245184118934146\right)$$

The opposite of -686.245184118934146 is 686.245184118934146.

$$1341+686.245184118934146$$

Add 1341 and 686.245184118934146 to get 2027.245184118934146.

$$2027.245184118934146$$

Factor

$$\frac{30977 \cdot 62299 \cdot 58359739 \cdot 3 ^ {2}}{2 ^ {14} \cdot 5 ^ {15}} = 2027\frac{122592059467136}{500000000000000} = 2027.2451841189343$$