Trigonometry Examples

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

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

Step 1

Rewrite the equation as

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

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

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

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

Step 2

Add

5^{2}

$5^{2}$ and

5^{2}

$5^{2}$ .

c^{2} = 2 \cdot 5^{2}

$c^{2} = 2 \cdot 5^{2}$

Step 3

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

c = \pm \sqrt{2 \cdot 5^{2}}

$c = \pm \sqrt{2 \cdot 5^{2}}$

Step 4

Simplify

\pm \sqrt{2 \cdot 5^{2}}

$\pm \sqrt{2 \cdot 5^{2}}$ .

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Raise

5

$5$ to the power of

2

$2$ .

c = \pm \sqrt{2 \cdot 25}

$c = \pm \sqrt{2 \cdot 25}$

Multiply

2

$2$ by

25

$25$ .

c = \pm \sqrt{50}

$c = \pm \sqrt{50}$

Rewrite

50

$50$ as

5^{2} \cdot 2

$5^{2} \cdot 2$ .

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Factor

25

$25$ out of

50

$50$ .

c = \pm \sqrt{25 (2)}

$c = \pm \sqrt{25 (2)}$

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

c = \pm \sqrt{5^{2} \cdot 2}

$c = \pm \sqrt{5^{2} \cdot 2}$

c = \pm \sqrt{5^{2} \cdot 2}

$c = \pm \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

c = \pm 5 \sqrt{2}

$c = \pm 5 \sqrt{2}$

c = \pm 5 \sqrt{2}

$c = \pm 5 \sqrt{2}$

Step 5

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

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First, use the positive value of the

\pm

$\pm$ to find the first solution.

c = 5 \sqrt{2}

$c = 5 \sqrt{2}$

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

c = - 5 \sqrt{2}

$c = - 5 \sqrt{2}$

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

c = 5 \sqrt{2}, - 5 \sqrt{2}

$c = 5 \sqrt{2}, - 5 \sqrt{2}$

c = 5 \sqrt{2}, - 5 \sqrt{2}

$c = 5 \sqrt{2}, - 5 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

c = 5 \sqrt{2}, - 5 \sqrt{2}

$c = 5 \sqrt{2}, - 5 \sqrt{2}$

Decimal Form:

c = 7.07106781 \dots, - 7.07106781 \dots

$c = 7.07106781 \dots, - 7.07106781 \dots$