Trigonometry Examples

\frac{11}{sin (77)} = \frac{x}{sin (45)}

$\frac{11}{\sin (77)} = \frac{x}{\sin (45)}$

Step 1

Rewrite the equation as

\frac{x}{sin (45)} = \frac{11}{sin (77)}

$\frac{x}{\sin (45)} = \frac{11}{\sin (77)}$ .

\frac{x}{sin (45)} = \frac{11}{sin (77)}

$\frac{x}{\sin (45)} = \frac{11}{\sin (77)}$

Step 2

Multiply both sides of the equation by

sin (45)

$\sin (45)$ .

sin (45) \frac{x}{sin (45)} = sin (45) \frac{11}{sin (77)}

$\sin (45) \frac{x}{\sin (45)} = \sin (45) \frac{11}{\sin (77)}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of

sin (45)

$\sin (45)$ .

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Step 3.1.1.1

Cancel the common factor.

$\sin (45) \frac{x}{\sin (45)} = \sin (45) \frac{11}{\sin (77)}$

Step 3.1.1.2

Rewrite the expression.

$x = \sin (45) \frac{11}{\sin (77)}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify

$\sin (45) \frac{11}{\sin (77)}$ .

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Step 3.2.1.1

The exact value of

$\sin (45)$ is

$\frac{\sqrt{2}}{2}$ .

$x = \frac{\sqrt{2}}{2} \cdot \frac{11}{\sin (77)}$

Step 3.2.1.2

Separate fractions.

$x = \frac{\sqrt{2}}{2} (\frac{11}{1} \cdot \frac{1}{\sin (77)})$

Step 3.2.1.3

Convert from

$\frac{1}{\sin (77)}$ to

$\csc (77)$ .

$x = \frac{\sqrt{2}}{2} (\frac{11}{1} \csc (77))$

Step 3.2.1.4

Divide

$11$ by

$1$ .

$x = \frac{\sqrt{2}}{2} (11 \csc (77))$

Step 3.2.1.5

Evaluate

$\csc (77)$ .

$x = \frac{\sqrt{2}}{2} (11 \cdot 1.0263041)$

Step 3.2.1.6

Multiply

$11$ by

$1.0263041$ .

$x = \frac{\sqrt{2}}{2} \cdot 11.28934518$

Step 3.2.1.7

Multiply

$\frac{\sqrt{2}}{2} \cdot 11.28934518$ .

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Step 3.2.1.7.1

Combine

$\frac{\sqrt{2}}{2}$ and

$11.28934518$ .

$x = \frac{\sqrt{2} \cdot 11.28934518}{2}$

Step 3.2.1.7.2

Multiply

$\sqrt{2}$ by

$11.28934518$ .

$x = \frac{15.96554507}{2}$

Step 3.2.1.8

Divide

$15.96554507$ by

$2$ .

$x = 7.98277253$