Solve 20^2+18^2+2*20*18*cos(80^circ)

$${ 20 }^{ 2 } + { 18 }^{ 2 } +2 \times 20 \times 18 \times \cos ( 80 ^ { \circ } )$$

Evaluate

$$849.0266879201898952$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(20)} ^ {2} + {(18)} ^ {2} + 2 \cdot 20 \cdot 18 \cdot 0.17364817766693041$$

Calculate 20 to the power of 2 and get 400.

$$400+18^{2}+2\times 20\times 18\times 0.17364817766693041$$

Calculate 18 to the power of 2 and get 324.

$$400+324+2\times 20\times 18\times 0.17364817766693041$$

Add 400 and 324 to get 724.

$$724+2\times 20\times 18\times 0.17364817766693041$$

Multiply 2 and 20 to get 40.

$$724+40\times 18\times 0.17364817766693041$$

Multiply 40 and 18 to get 720.

$$724+720\times 0.17364817766693041$$

Multiply 720 and 0.17364817766693041 to get 125.0266879201898952.

$$724+125.0266879201898952$$

Add 724 and 125.0266879201898952 to get 849.0266879201898952.

$$849.0266879201898952$$

Factor

$$\frac{127 \cdot 38453 \cdot 4435078651 \cdot 7 ^ {2}}{2 ^ {13} \cdot 5 ^ {16}} = 849\frac{33359900237312}{1250000000000000} = 849.0266879201898$$