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Welcome to the article Solve for tex c tex using the Pythagorean theorem tex begin aligned a 2 b 2 c 2 12 2 13 2 c 2 c. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!

Solve for [tex]c[/tex] using the Pythagorean theorem:

[tex]
\begin{aligned}
a^2 + b^2 & = c^2 \\
12^2 + 13^2 & = c^2 \\
c^2 & = 144 + 169 \\
c^2 & = 313
\end{aligned}
[/tex]

Find [tex]c[/tex] by taking the square root of 313.

Answer :

Alright, let's go through the solution step-by-step!

We have an equation based on the Pythagorean theorem:
[tex]\[ a^2 + b^2 = c^2 \][/tex]

The values given are [tex]\( a = 12 \)[/tex] and [tex]\( b = 13 \)[/tex]. We need to find [tex]\( c^2 \)[/tex].

1. Calculate [tex]\( a^2 \)[/tex]:
[tex]\[ a^2 = 12^2 = 144 \][/tex]

2. Calculate [tex]\( b^2 \)[/tex]:
[tex]\[ b^2 = 13^2 = 169 \][/tex]

3. Use the Pythagorean theorem to find [tex]\( c^2 \)[/tex]:
Add [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex] together:
[tex]\[ c^2 = 144 + 169 \][/tex]
[tex]\[ c^2 = 313 \][/tex]

So the result is [tex]\( c^2 = 313 \)[/tex]. This means that the square of the hypotenuse [tex]\( c \)[/tex] is 313.

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Rewritten by : Brahmana