Trigonometry Examples

$\tan (12) = \frac{10}{x}$

Step 1

Rewrite the equation as $\frac{10}{x} = \tan (12)$ .

$\frac{10}{x} = \tan (12)$

Step 2

Evaluate $\tan (12)$ .

$\frac{10}{x} = 0.21255656$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

Step 3.2

The LCM of one and any expression is the expression.

$x$

Step 4

Multiply each term in $\frac{10}{x} = 0.21255656$ by $x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{10}{x} = 0.21255656$ by $x$ .

$\frac{10}{x} x = 0.21255656 x$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{10}{x} x = 0.21255656 x$

Step 4.2.1.2

Rewrite the expression.

$10 = 0.21255656 x$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $0.21255656 x = 10$ .

$0.21255656 x = 10$

Step 5.2

Divide each term in $0.21255656 x = 10$ by $0.21255656$ and simplify.

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Step 5.2.1

Divide each term in $0.21255656 x = 10$ by $0.21255656$ .

$\frac{0.21255656 x}{0.21255656} = \frac{10}{0.21255656}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $0.21255656$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{0.21255656 x}{0.21255656} = \frac{10}{0.21255656}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{0.21255656}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $10$ by $0.21255656$ .

$x = 47.04630109$