Precalculus Examples

$\frac{x}{\sin (52.2)} = \frac{32.9}{\sin (115.4)}$

Step 1

Multiply both sides of the equation by $\sin (52.2)$ .

$\sin (52.2) \frac{x}{\sin (52.2)} = \sin (52.2) \frac{32.9}{\sin (115.4)}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $\sin (52.2)$ .

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Step 2.1.1.1

Cancel the common factor.

$\sin (52.2) \frac{x}{\sin (52.2)} = \sin (52.2) \frac{32.9}{\sin (115.4)}$

Step 2.1.1.2

Rewrite the expression.

$x = \sin (52.2) \frac{32.9}{\sin (115.4)}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\sin (52.2) \frac{32.9}{\sin (115.4)}$ .

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Step 2.2.1.1

Separate fractions.

$x = \sin (52.2) (\frac{32.9}{1} \cdot \frac{1}{\sin (115.4)})$

Step 2.2.1.2

Convert from $\frac{1}{\sin (115.4)}$ to $\csc (115.4)$ .

$x = \sin (52.2) (\frac{32.9}{1} \csc (115.4))$

Step 2.2.1.3

Divide $32.9$ by $1$ .

$x = \sin (52.2) (32.9 \csc (115.4))$

Step 2.2.1.4

Multiply $32.9$ by $\csc (115.4)$ .

$x = \sin (52.2) \cdot 36.4205852$

Step 2.2.1.5

Multiply $\sin (52.2)$ by $36.4205852$ .

$x = 28.77790795$