Trigonometry Examples

$a^{2} + b^{2} = 10^{2}$

Step 1

Raise $10$ to the power of $2$ .

$a^{2} + b^{2} = 100$

Step 2

Subtract $a^{2}$ from both sides of the equation.

$b^{2} = 100 - a^{2}$

Step 3

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

$b = \pm \sqrt{100 - a^{2}}$

Step 4

Simplify $\pm \sqrt{100 - a^{2}}$ .

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Step 4.1

Rewrite $100$ as $10^{2}$ .

$b = \pm \sqrt{10^{2} - a^{2}}$

Step 4.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 10$ and $b = a$ .

$b = \pm \sqrt{(10 + a) (10 - a)}$

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.

$b = \sqrt{(10 + a) (10 - a)}$

Step 5.2

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

$b = - \sqrt{(10 + a) (10 - a)}$

Step 5.3

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

$b = \sqrt{(10 + a) (10 - a)}$

$b = - \sqrt{(10 + a) (10 - a)}$

$b = \sqrt{(10 + a) (10 - a)}$

$b = - \sqrt{(10 + a) (10 - a)}$