Solve sin(410)=x/sqrt{35}

$$\sin ( 410 ) = \frac { x } { \sqrt { 35 } }$$

Solve for x

$$x = \frac{3830222215594889 \sqrt{35}}{5000000000000000} = 4\frac{2659900214459944}{5000000000000000} \approx 4.531980043$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$0.7660444431189778 = \frac{x}{\sqrt{35}}$$

Rationalize the denominator of \frac{x}{\sqrt{35}} by multiplying numerator and denominator by \sqrt{35}.

$$0.7660444431189778=\frac{x\sqrt{35}}{\left(\sqrt{35}\right)^{2}}$$

The square of \sqrt{35} is 35.

$$0.7660444431189778=\frac{x\sqrt{35}}{35}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x\sqrt{35}}{35}=0.7660444431189778$$

Multiply both sides by 35.

$$x\sqrt{35}=0.7660444431189778\times 35$$

Multiply 0.7660444431189778 and 35 to get 26.811555509164223.

$$x\sqrt{35}=26.811555509164223$$

The equation is in standard form.

$$\sqrt{35}x=26.811555509164223$$

Divide both sides by \sqrt{35}.

$$\frac{\sqrt{35}x}{\sqrt{35}}=\frac{26.811555509164223}{\sqrt{35}}$$

Dividing by \sqrt{35} undoes the multiplication by \sqrt{35}.

$$x=\frac{26.811555509164223}{\sqrt{35}}$$

Divide 26.811555509164223 by \sqrt{35}.

$$x=\frac{3830222215594889\sqrt{35}}{5000000000000000}$$