Trigonometry Examples

$\tan (30) = \frac{x}{10 \sqrt{3}}$

Step 1

Rewrite the equation as $\frac{x}{10 \sqrt{3}} = \tan (30)$ .

$\frac{x}{10 \sqrt{3}} = \tan (30)$

Step 2

Multiply both sides of the equation by $10 \sqrt{3}$ .

$10 \sqrt{3} \frac{x}{10 \sqrt{3}} = 10 \sqrt{3} \tan (30)$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $10 \sqrt{3}$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$10 \sqrt{3} \frac{x}{10 \sqrt{3}} = 10 \sqrt{3} \tan (30)$

Step 3.1.1.2

Rewrite the expression.

$x = 10 \sqrt{3} \tan (30)$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $10 \sqrt{3} \tan (30)$ .

Tap for more steps...

Step 3.2.1.1

The exact value of $\tan (30)$ is $\frac{\sqrt{3}}{3}$ .

$x = 10 \sqrt{3} \frac{\sqrt{3}}{3}$

Step 3.2.1.2

Multiply $10 \sqrt{3} \frac{\sqrt{3}}{3}$ .

Tap for more steps...

Step 3.2.1.2.1

Combine $\frac{\sqrt{3}}{3}$ and $10$ .

$x = \frac{\sqrt{3} \cdot 10}{3} \sqrt{3}$

Step 3.2.1.2.2

Combine $\frac{\sqrt{3} \cdot 10}{3}$ and $\sqrt{3}$ .

$x = \frac{\sqrt{3} \cdot 10 \sqrt{3}}{3}$

Step 3.2.1.2.3

Raise $\sqrt{3}$ to the power of $1$ .

$x = \frac{10 ({\sqrt{3}}^{1} \sqrt{3})}{3}$

Step 3.2.1.2.4

Raise $\sqrt{3}$ to the power of $1$ .

$x = \frac{10 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}{3}$

Step 3.2.1.2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{10 {\sqrt{3}}^{1 + 1}}{3}$

Step 3.2.1.2.6

Add $1$ and $1$ .

$x = \frac{10 {\sqrt{3}}^{2}}{3}$

Step 3.2.1.3

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Step 3.2.1.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$x = \frac{10 {(3^{\frac{1}{2}})}^{2}}{3}$

Step 3.2.1.3.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \frac{10 \cdot 3^{\frac{1}{2} \cdot 2}}{3}$

Step 3.2.1.3.3

Combine $\frac{1}{2}$ and $2$ .

$x = \frac{10 \cdot 3^{\frac{2}{2}}}{3}$

Step 3.2.1.3.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.3.4.1

Cancel the common factor.

$x = \frac{10 \cdot 3^{\frac{2}{2}}}{3}$

Step 3.2.1.3.4.2

Rewrite the expression.

$x = \frac{10 \cdot 3^{1}}{3}$

Step 3.2.1.3.5

Evaluate the exponent.

$x = \frac{10 \cdot 3}{3}$

Step 3.2.1.4

Simplify the expression.

Tap for more steps...

Step 3.2.1.4.1

Multiply $10$ by $3$ .

$x = \frac{30}{3}$

Step 3.2.1.4.2

Divide $30$ by $3$ .

$x = 10$