Solve 8^2+5^2-2*8*5cos45^circ

$$8 ^ { 2 } + 5 ^ { 2 } - 2 \cdot 8 \cdot 5 \cos 45 ^ { \circ }$$

Evaluate

$$89-40\sqrt{2}\approx 32.431457505$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$64+5^{2}-2\times 5\times 8\cos(45)$$

Calculate 5 to the power of 2 and get 25.

$$64+25-2\times 5\times 8\cos(45)$$

Add 64 and 25 to get 89.

$$89-2\times 5\times 8\cos(45)$$

Multiply 2 and 5 to get 10.

$$89-10\times 8\cos(45)$$

Multiply 10 and 8 to get 80.

$$89-80\cos(45)$$

Get the value of \cos(45) from trigonometric values table.

$$89-80\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 80 and 2.

$$89-40\sqrt{2}$$