Trigonometry Examples

$\frac{x}{\sin (110)} = \frac{200}{\sin (140)}$

Step 1

Simplify $\frac{x}{\sin (110)}$ .

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Step 1.1

Separate fractions.

$\frac{x}{1} \cdot \frac{1}{\sin (110)} = \frac{200}{\sin (140)}$

Step 1.2

Convert from $\frac{1}{\sin (110)}$ to $\csc (110)$ .

$\frac{x}{1} \csc (110) = \frac{200}{\sin (140)}$

Step 1.3

Divide $x$ by $1$ .

$x \csc (110) = \frac{200}{\sin (140)}$

Step 1.4

Evaluate $\csc (110)$ .

$x \cdot 1.06417777 = \frac{200}{\sin (140)}$

Step 1.5

Move $1.06417777$ to the left of $x$ .

$1.06417777 x = \frac{200}{\sin (140)}$

Step 2

Simplify $\frac{200}{\sin (140)}$ .

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Step 2.1

Separate fractions.

$1.06417777 x = \frac{200}{1} \cdot \frac{1}{\sin (140)}$

Step 2.2

Convert from $\frac{1}{\sin (140)}$ to $\csc (140)$ .

$1.06417777 x = \frac{200}{1} \csc (140)$

Step 2.3

Divide $200$ by $1$ .

$1.06417777 x = 200 \csc (140)$

Step 2.4

Evaluate $\csc (140)$ .

$1.06417777 x = 200 \cdot 1.55572382$

Step 2.5

Multiply $200$ by $1.55572382$ .

$1.06417777 x = 311.14476537$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 9.02691044$

Step 4