Trigonometry Examples

$112 = 135^{2} + a^{2}$

Step 1

Rewrite the equation as $135^{2} + a^{2} = 112$ .

$135^{2} + a^{2} = 112$

Step 2

Raise $135$ to the power of $2$ .

$18225 + a^{2} = 112$

Step 3

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

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Step 3.1

Subtract $18225$ from both sides of the equation.

$a^{2} = 112 - 18225$

Step 3.2

Subtract $18225$ from $112$ .

$a^{2} = - 18113$

Step 4

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

$a = \pm \sqrt{- 18113}$

Step 5

Simplify $\pm \sqrt{- 18113}$ .

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Step 5.1

Rewrite $- 18113$ as $- 1 (18113)$ .

$a = \pm \sqrt{- 1 (18113)}$

Step 5.2

Rewrite $\sqrt{- 1 (18113)}$ as $\sqrt{- 1} \cdot \sqrt{18113}$ .

$a = \pm \sqrt{- 1} \cdot \sqrt{18113}$

Step 5.3

Rewrite $\sqrt{- 1}$ as $i$ .

$a = \pm i \sqrt{18113}$

Step 6

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

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Step 6.1

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

$a = i \sqrt{18113}$

Step 6.2

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

$a = - i \sqrt{18113}$

Step 6.3

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

$a = i \sqrt{18113}, - i \sqrt{18113}$