Trigonometry Examples

$a^{2} + 5^{2} = 6^{2}$

Step 1

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

$a^{2} + 25 = 6^{2}$

Step 2

Raise $6$ to the power of $2$ .

$a^{2} + 25 = 36$

Step 3

Move all terms not containing $a$ to the right side of the equation.

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Step 3.1

Subtract $25$ from both sides of the equation.

$a^{2} = 36 - 25$

Step 3.2

Subtract $25$ from $36$ .

$a^{2} = 11$

Step 4

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

$a = \pm \sqrt{11}$

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.

$a = \sqrt{11}$

Step 5.2

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

$a = - \sqrt{11}$

Step 5.3

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

$a = \sqrt{11}, - \sqrt{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \sqrt{11}, - \sqrt{11}$

Decimal Form:

$a = 3.31662479 \dots, - 3.31662479 \dots$