Solve sqrt{2^2+5^2-2*2*5cos(30-120)}

$$\sqrt{ { 2 }^{ 2 } + { 5 }^{ 2 } -2 \cdot 2 \cdot 5 \cos ( 30-120 ) }$$

Evaluate

$$\sqrt{29}\approx 5.385164807$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+5^{2}-2\times 2\times 5\cos(30-120)}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{4+25-2\times 2\times 5\cos(30-120)}$$

Add 4 and 25 to get 29.

$$\sqrt{29-2\times 2\times 5\cos(30-120)}$$

Multiply 2 and 2 to get 4.

$$\sqrt{29-4\times 5\cos(30-120)}$$

Multiply 4 and 5 to get 20.

$$\sqrt{29-20\cos(30-120)}$$

Subtract 120 from 30 to get -90.

$$\sqrt{29-20\cos(-90)}$$

Use the property \cos(-x)=\cos(x).

$$\sqrt{29-20\cos(90)}$$

Get the value of \cos(90) from trigonometric values table.

$$\sqrt{29-20\times 0}$$

Multiply 20 and 0 to get 0.

$$\sqrt{29-0}$$

Subtract 0 from 29 to get 29.

$$\sqrt{29}$$