Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth. c = meters

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 12\) and \(b=16\).
\[c^{2}=12^{2}+16^{2}\]

Step2: Calculate squares

\[12^{2}=144\] and \[16^{2}=256\]. Then \(c^{2}=144 + 256\).
\[c^{2}=400\]

Step3: Find the square - root

Take the square - root of both sides. Since \(c>0\) (length), \(c=\sqrt{400}\).
\[c = 20\]

Answer:

20