Trigonometry Examples

$5^{2} + 1^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 5^{2} + 1^{2}$ .

$c^{2} = 5^{2} + 1^{2}$

Step 2

One to any power is one.

$c^{2} = 5^{2} + 1$

Step 3

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

$c = \pm \sqrt{5^{2} + 1}$

Step 4

Simplify $\pm \sqrt{5^{2} + 1}$ .

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Step 4.1

Raise $5$ to the power of $2$ .

$c = \pm \sqrt{25 + 1}$

Step 4.2

Add $25$ and $1$ .

$c = \pm \sqrt{26}$

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.

$c = \sqrt{26}$

Step 5.2

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

$c = - \sqrt{26}$

Step 5.3

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

$c = \sqrt{26}, - \sqrt{26}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$c = \sqrt{26}, - \sqrt{26}$

Decimal Form:

$c = 5.09901951 \dots, - 5.09901951 \dots$