Trigonometry Examples

$3^{2} + 3^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 3^{2} + 3^{2}$ .

$c^{2} = 3^{2} + 3^{2}$

Step 2

Add $3^{2}$ and $3^{2}$ .

$c^{2} = 2 \cdot 3^{2}$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$c = \pm \sqrt{2 \cdot 3^{2}}$

Step 4

Simplify $\pm \sqrt{2 \cdot 3^{2}}$ .

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Step 4.1

Raise $3$ to the power of $2$ .

$c = \pm \sqrt{2 \cdot 9}$

Step 4.2

Multiply $2$ by $9$ .

$c = \pm \sqrt{18}$

Step 4.3

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 4.3.1

Factor $9$ out of $18$ .

$c = \pm \sqrt{9 (2)}$

Step 4.3.2

Rewrite $9$ as $3^{2}$ .

$c = \pm \sqrt{3^{2} \cdot 2}$

Step 4.4

Pull terms out from under the radical.

$c = \pm 3 \sqrt{2}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$c = 3 \sqrt{2}$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$c = - 3 \sqrt{2}$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$c = 3 \sqrt{2}, - 3 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$c = 3 \sqrt{2}, - 3 \sqrt{2}$

Decimal Form:

$c = 4.24264068 \dots, - 4.24264068 \dots$