Solve for B cos(B)=46^2+58^2-(70^2)÷24658

$\cos (B) = 46^{2} + 58^{2} - 70^{2} \div 2 \cdot 46 \cdot 58$

Simplify $46^{2} + 58^{2} - 70^{2} \div 2 \cdot 46 \cdot 58$ .

Simplify each term.

Raise $46$ to the power of $2$ .

$\cos (B) = 2116 + 58^{2} - 70^{2} \div 2 \cdot 46 \cdot 58$

Raise $58$ to the power of $2$ .

$\cos (B) = 2116 + 3364 - 70^{2} \div 2 \cdot 46 \cdot 58$

Raise $70$ to the power of $2$ .

$\cos (B) = 2116 + 3364 - 4900 \div 2 \cdot 46 \cdot 58$

Cancel the common factor of $2$ .

Move the leading negative in $- 4900 \div 2$ into the numerator.

$\cos (B) = 2116 + 3364 + - 4900 \div 2 \cdot 46 \cdot 58$

Factor $2$ out of $46$ .

$\cos (B) = 2116 + 3364 + - 4900 \div 2 \cdot (2 (23)) \cdot 58$

Cancel the common factor.

$\cos (B) = 2116 + 3364 + - 4900 \div 2 \cdot (2 \cdot 23) \cdot 58$

Rewrite the expression.

$\cos (B) = 2116 + 3364 - 4900 \cdot 23 \cdot 58$

Multiply $- 4900$ by $23$ .

$\cos (B) = 2116 + 3364 - 112700 \cdot 58$

Multiply $- 112700$ by $58$ .

$\cos (B) = 2116 + 3364 - 6536600$

Simplify by adding and subtracting.

Add $2116$ and $3364$ .

$\cos (B) = 5480 - 6536600$

Subtract $6536600$ from $5480$ .

$\cos (B) = - 6531120$

The range of cosine is $- 1 \leq y \leq 1$ . Since $- 6531120$ does not fall in this range, there is no solution.

No solution

Solve for B cos(B)=46^2+58^2-(70^2)÷2*46*58