Solve (12)^2+(22)^2-2*12*22*cos75^circ

$$( 12 ) ^ { 2 } + ( 22 ) ^ { 2 } - 2 \times 12 \times 22 \times \cos 75 ^ { \circ }$$

Evaluate

$$491.34354418586904928$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(12)} ^ {2} + {(22)} ^ {2} - 2 \cdot 12 \cdot 22 \cdot 0.25881904510252074$$

Calculate 12 to the power of 2 and get 144.

$$144+22^{2}-2\times 12\times 22\times 0.25881904510252074$$

Calculate 22 to the power of 2 and get 484.

$$144+484-2\times 12\times 22\times 0.25881904510252074$$

Add 144 and 484 to get 628.

$$628-2\times 12\times 22\times 0.25881904510252074$$

Multiply 2 and 12 to get 24.

$$628-24\times 22\times 0.25881904510252074$$

Multiply 24 and 22 to get 528.

$$628-528\times 0.25881904510252074$$

Multiply 528 and 0.25881904510252074 to get 136.65645581413095072.

$$628-136.65645581413095072$$

Subtract 136.65645581413095072 from 628 to get 491.34354418586904928.

$$491.34354418586904928$$

Factor

$$\frac{199 \cdot 2111 \cdot 3187 \cdot 1146863953}{2 ^ {12} \cdot 5 ^ {17}} = 491\frac{1073575580840704}{3125000000000000} = 491.343544185869$$