Solve 73^2+(42)^2-2(73(42))cos81

$$73 ^ { 2 } + ( 42 ) ^ { 2 } - 2 ( 73 ( 42 ) ) \cos 81$$

Evaluate

$$6133.74386037330399856$$

Solution Steps

Evaluate trigonometric functions in the problem

$$73 ^ {2} + {(42)} ^ {2} - 2 {(73 {(42)})} 0.15643446504023092$$

Calculate 73 to the power of 2 and get 5329.

$$5329+42^{2}-2\times 73\times 42\times 0.15643446504023092$$

Calculate 42 to the power of 2 and get 1764.

$$5329+1764-2\times 73\times 42\times 0.15643446504023092$$

Add 5329 and 1764 to get 7093.

$$7093-2\times 73\times 42\times 0.15643446504023092$$

Multiply 2 and 73 to get 146.

$$7093-146\times 42\times 0.15643446504023092$$

Multiply 146 and 42 to get 6132.

$$7093-6132\times 0.15643446504023092$$

Multiply 6132 and 0.15643446504023092 to get 959.25613962669600144.

$$7093-959.25613962669600144$$

Subtract 959.25613962669600144 from 7093 to get 6133.74386037330399856.

$$6133.74386037330399856$$

Factor

$$\frac{11 \cdot 478493 \cdot 7283453966617}{2 ^ {13} \cdot 5 ^ {17}} = 6133\frac{4649127333150720}{6250000000000000} = 6133.743860373304$$