Trigonometry Examples

$\frac{\sin (28)}{x} = \frac{\sin (110)}{42}$

Step 1

Factor each term.

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Step 1.1

Evaluate $\sin (28)$ .

$\frac{0.46947156}{x} = \frac{\sin (110)}{42}$

Step 1.2

Evaluate $\sin (110)$ .

$\frac{0.46947156}{x} = \frac{0.93969262}{42}$

Step 1.3

Divide $0.93969262$ by $42$ .

$\frac{0.46947156}{x} = 0.02237363$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$x, 1$

Step 2.2

The LCM of one and any expression is the expression.

$x$

Step 3

Multiply each term in $\frac{0.46947156}{x} = 0.02237363$ by $x$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{0.46947156}{x} = 0.02237363$ by $x$ .

$\frac{0.46947156}{x} x = 0.02237363 x$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.46947156}{x} x = 0.02237363 x$

Step 3.2.1.2

Rewrite the expression.

$0.46947156 = 0.02237363 x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $0.02237363 x = 0.46947156$ .

$0.02237363 x = 0.46947156$

Step 4.2

Divide each term in $0.02237363 x = 0.46947156$ by $0.02237363$ and simplify.

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Step 4.2.1

Divide each term in $0.02237363 x = 0.46947156$ by $0.02237363$ .

$\frac{0.02237363 x}{0.02237363} = \frac{0.46947156}{0.02237363}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $0.02237363$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{0.02237363 x}{0.02237363} = \frac{0.46947156}{0.02237363}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0.46947156}{0.02237363}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $0.46947156$ by $0.02237363$ .

$x = 20.98325048$