Solve for F1 F_1cos(45)+F_2cos(30)=500

$F_{1} \cdot \cos (45) + F_{2} \cdot \cos (30) = 500$

Step 1

Simplify the left side.

Simplify each term.

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$F_{1} \cdot \frac{\sqrt{2}}{2} + F_{2} \cdot \cos (30) = 500$

Combine $F_{1}$ and $\frac{\sqrt{2}}{2}$ .

$\frac{F_{1} \sqrt{2}}{2} + F_{2} \cdot \cos (30) = 500$

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{F_{1} \sqrt{2}}{2} + F_{2} \cdot \frac{\sqrt{3}}{2} = 500$

Combine $F_{2}$ and $\frac{\sqrt{3}}{2}$ .

$\frac{F_{1} \sqrt{2}}{2} + \frac{F_{2} \sqrt{3}}{2} = 500$

Step 2

Move all terms not containing $F「+1」$ to the right side of the equation.

Subtract $\frac{F_{1} \sqrt{2}}{2}$ from both sides of the equation.

$\frac{F_{2} \sqrt{3}}{2} = 500 - \frac{F_{1} \sqrt{2}}{2}$

Subtract $\frac{F_{2} \sqrt{3}}{2}$ from both sides of the equation.

$0 = 500 - \frac{F_{1} \sqrt{2}}{2} - \frac{F_{2} \sqrt{3}}{2}$

Step 3

Rewrite the equation as $500 - \frac{F_{1} \sqrt{2}}{2} - \frac{F_{2} \sqrt{3}}{2} = 0$ .

$500 - \frac{F_{1} \sqrt{2}}{2} - \frac{F_{2} \sqrt{3}}{2} = 0$

Solve for F1 F_1*cos(45)+F_2*cos(30)=500