Solve for θ 100cos(theta)=w(5/13)

$100 \cos (θ) = w (\frac{5}{13})$

Step 1

Combine $w$ and $\frac{5}{13}$ .

$100 \cos (θ) = \frac{w \cdot 5}{13}$

Step 2

Divide each term in $100 \cos (θ) = \frac{w \cdot 5}{13}$ by $100$ and simplify.

Divide each term in $100 \cos (θ) = \frac{w \cdot 5}{13}$ by $100$ .

$\frac{100 \cos (θ)}{100} = \frac{\frac{w \cdot 5}{13}}{100}$

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$\frac{100 \cos (θ)}{100} = \frac{\frac{w \cdot 5}{13}}{100}$

Divide $\cos (θ)$ by $1$ .

$\cos (θ) = \frac{\frac{w \cdot 5}{13}}{100}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$\cos (θ) = \frac{w \cdot 5}{13} \cdot \frac{1}{100}$

Cancel the common factor of $5$ .

Factor $5$ out of $w \cdot 5$ .

$\cos (θ) = \frac{5 \cdot w}{13} \cdot \frac{1}{100}$

Factor $5$ out of $100$ .

$\cos (θ) = \frac{5 \cdot w}{13} \cdot \frac{1}{5 (20)}$

Cancel the common factor.

$\cos (θ) = \frac{5 \cdot w}{13} \cdot \frac{1}{5 \cdot 20}$

Rewrite the expression.

$\cos (θ) = \frac{w}{13} \cdot \frac{1}{20}$

Multiply $\frac{w}{13}$ by $\frac{1}{20}$ .

$\cos (θ) = \frac{w}{13 \cdot 20}$

Multiply $13$ by $20$ .

$\cos (θ) = \frac{w}{260}$

Step 3

Take the inverse cosine of both sides of the equation to extract $θ$ from inside the cosine.

$θ = \arccos (\frac{w}{260})$