Solve tan(22.5)=x/frac{1{sqrt{2}}a}

$$\tan ( 22.5 ) = \frac{ x }{ \frac{ 1 }{ \sqrt{ 2 } } a }$$

Solve for a

$$a=\frac{100000000000000000\sqrt{2}x}{41421356237309503}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$0.41421356237309503 = \frac{x}{\frac{1}{\sqrt{2}} a}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$0.41421356237309503=\frac{x}{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}a}$$

The square of \sqrt{2} is 2.

$$0.41421356237309503=\frac{x}{\frac{\sqrt{2}}{2}a}$$

Express \frac{\sqrt{2}}{2}a as a single fraction.

$$0.41421356237309503=\frac{x}{\frac{\sqrt{2}a}{2}}$$

Divide x by \frac{\sqrt{2}a}{2} by multiplying x by the reciprocal of \frac{\sqrt{2}a}{2}.

$$0.41421356237309503=\frac{x\times 2}{\sqrt{2}a}$$

Factor the expressions that are not already factored in \frac{x\times 2}{\sqrt{2}a}.

$$0.41421356237309503=\frac{2x}{\sqrt{2}a}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$0.41421356237309503=\frac{\sqrt{2}x}{a}$$

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

$$\frac{\sqrt{2}x}{a}=0.41421356237309503$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$\sqrt{2}x=0.41421356237309503a$$

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

$$0.41421356237309503a=\sqrt{2}x$$

Divide both sides of the equation by 0.41421356237309503, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.41421356237309503a}{0.41421356237309503}=\frac{\sqrt{2}x}{0.41421356237309503}$$

Dividing by 0.41421356237309503 undoes the multiplication by 0.41421356237309503.

$$a=\frac{\sqrt{2}x}{0.41421356237309503}$$

Divide \sqrt{2}x by 0.41421356237309503 by multiplying \sqrt{2}x by the reciprocal of 0.41421356237309503.

$$a=\frac{100000000000000000\sqrt{2}x}{41421356237309503}$$

Variable a cannot be equal to 0.

$$a=\frac{100000000000000000\sqrt{2}x}{41421356237309503}\text{, }a\neq 0$$

Solve for x

$$x=\frac{41421356237309503\sqrt{2}a}{200000000000000000}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$0.41421356237309503 = \frac{x}{\frac{1}{\sqrt{2}} a}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$0.41421356237309503=\frac{x}{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}a}$$

The square of \sqrt{2} is 2.

$$0.41421356237309503=\frac{x}{\frac{\sqrt{2}}{2}a}$$

Express \frac{\sqrt{2}}{2}a as a single fraction.

$$0.41421356237309503=\frac{x}{\frac{\sqrt{2}a}{2}}$$

Divide x by \frac{\sqrt{2}a}{2} by multiplying x by the reciprocal of \frac{\sqrt{2}a}{2}.

$$0.41421356237309503=\frac{x\times 2}{\sqrt{2}a}$$

Factor the expressions that are not already factored in \frac{x\times 2}{\sqrt{2}a}.

$$0.41421356237309503=\frac{2x}{\sqrt{2}a}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$0.41421356237309503=\frac{\sqrt{2}x}{a}$$

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

$$\frac{\sqrt{2}x}{a}=0.41421356237309503$$

Multiply both sides of the equation by a.

$$\sqrt{2}x=0.41421356237309503a$$

The equation is in standard form.

$$\sqrt{2}x=\frac{41421356237309503a}{100000000000000000}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{41421356237309503a}{100000000000000000\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$x=\frac{41421356237309503a}{100000000000000000\sqrt{2}}$$

Divide \frac{41421356237309503a}{100000000000000000} by \sqrt{2}.

$$x=\frac{41421356237309503\sqrt{2}a}{200000000000000000}$$