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3 years ago

The length of the hypotenuse is

Mathematics

1 answer:

pychu [463]3 years ago

4 0

Hello! The length of hypotenuse is 39

Make sure to read an explanation so you will be able to understand your problem clearly.

If you have any questions about the answer and explanation, feel free to comment and ask below.

Step-by-step explanation:

We can find a missing hypotenuse by using Pythagorean Theorem. Pythagorean Theorem can help finding length of a right-angle triangle. The formula is in the box below:

$\large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }$

a-term and b-term can be opposite or adjacent. But remember that c-term must be hypotenuse only.

Since we want to find a missing hypotenuse, we can substitute these numbers in the formula.

$\large{ {36}^{2} + {15}^{2} = {c}^{2} } \\ \large{1296 + 225 = {c}^{2} } \\ \large{1521 = {c}^{2} } \\ \large{ \sqrt{1521} = c} \\ \large{39 = c}$

Hence, the missing hypotenuse is 39.

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$\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \frac{9(|x-8|)}{9} < \frac{36}{9} \end{gathered}$}$

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$\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}$

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The length of the hypotenuse is ​

The length of the hypotenuse is