Solve for F -250(sin(45))-Fsin(30)=0

$- 250 \cdot (\sin (45)) - F \cdot \sin (30) = 0$

Step 1

Simplify each term.

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

$- 250 \cdot \frac{\sqrt{2}}{2} - F \cdot \sin (30) = 0$

Cancel the common factor of $2$ .

Factor $2$ out of $- 250$ .

$2 (- 125) \cdot \frac{\sqrt{2}}{2} - F \cdot \sin (30) = 0$

Cancel the common factor.

$2 \cdot - 125 \cdot \frac{\sqrt{2}}{2} - F \cdot \sin (30) = 0$

Rewrite the expression.

$- 125 \cdot \sqrt{2} - F \cdot \sin (30) = 0$

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$- 125 \sqrt{2} - F \cdot \frac{1}{2} = 0$

Combine $\frac{1}{2}$ and $F$ .

$- 125 \sqrt{2} - \frac{F}{2} = 0$

Step 2

Add $125 \sqrt{2}$ to both sides of the equation.

$- \frac{F}{2} = 125 \sqrt{2}$

Step 3

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{F}{2}) = - 2 (125 \sqrt{2})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{F}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{F}{2}$ into the numerator.

$- 2 \frac{- F}{2} = - 2 (125 \sqrt{2})$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- F}{2} = - 2 (125 \sqrt{2})$

Cancel the common factor.

$2 \cdot - 1 \frac{- F}{2} = - 2 (125 \sqrt{2})$

Rewrite the expression.

$- - F = - 2 (125 \sqrt{2})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 F = - 2 (125 \sqrt{2})$

Multiply $F$ by $1$ .

$F = - 2 (125 \sqrt{2})$

Simplify the right side.

Multiply $125$ by $- 2$ .

$F = - 250 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$F = - 250 \sqrt{2}$

Decimal Form:

$F = - 353.55339059 \dots$

Solve for F -250*(sin(45))-F*sin(30)=0

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Solve for F -250(sin(45))-Fsin(30)=0