Solve 400^2+500^2-2*400*500cos(20^circ)

$${ 400 }^{ 2 } + { 500 }^{ 2 } -2 \cdot 400 \cdot 500 \cos ( 20 ^ { \circ } )$$

Evaluate

$$34122.95168563664$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(400)} ^ {2} + {(500)} ^ {2} - 2 \cdot 400 \cdot 500 \cdot 0.9396926207859084$$

Calculate 400 to the power of 2 and get 160000.

$$160000+500^{2}-2\times 400\times 500\times 0.9396926207859084$$

Calculate 500 to the power of 2 and get 250000.

$$160000+250000-2\times 400\times 500\times 0.9396926207859084$$

Add 160000 and 250000 to get 410000.

$$410000-2\times 400\times 500\times 0.9396926207859084$$

Multiply 2 and 400 to get 800.

$$410000-800\times 500\times 0.9396926207859084$$

Multiply 800 and 500 to get 400000.

$$410000-400000\times 0.9396926207859084$$

Multiply 400000 and 0.9396926207859084 to get 375877.04831436336.

$$410000-375877.04831436336$$

Subtract 375877.04831436336 from 410000 to get 34122.95168563664.

$$34122.95168563664$$

Factor

$$\frac{23 \cdot 325447 \cdot 28491709}{2 ^ {7} \cdot 5 ^ {11}} = 34122\frac{5948035229}{6250000000} = 34122.95168563664$$