Solve for h 13.3 = square root of 11.3^2+h^2

$13.3 = \sqrt{{11.3}^{2} + h^{2}}$

Rewrite the equation as $\sqrt{{11.3}^{2} + h^{2}} = 13.3$ .

$\sqrt{{11.3}^{2} + h^{2}} = 13.3$

To remove the radical on the left side of the equation, square both sides of the equation.

${(\sqrt{{11.3}^{2} + h^{2}})}^{2} = {(13.3)}^{2}$

Simplify each side of the equation.

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Simplify the left side of the equation.

${11.3}^{2} + h^{2} = {(13.3)}^{2}$

Raise $13.3$ to the power of $2$ .

${11.3}^{2} + h^{2} = 176.89$

Solve for $h$ .

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Raise $11.3$ to the power of $2$ .

$127.69 + h^{2} = 176.89$

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

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Subtract $127.69$ from both sides of the equation.

$h^{2} = 176.89 - 127.69$

Subtract $127.69$ from $176.89$ .

$h^{2} = 49.2$

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

$h = \pm \sqrt{49.2}$

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 $\pm$ to find the first solution.

$h = \sqrt{49.2}$

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

$h = - \sqrt{49.2}$

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

$h = \sqrt{49.2}, - \sqrt{49.2}$

The result can be shown in multiple forms.

Exact Form:

$h = \sqrt{49.2}, - \sqrt{49.2}$

Decimal Form:

$h = 7.01427116 \dots, - 7.01427116 \dots$

Solve for h 13.3 = square root of 11.3^2+h^2

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