Answer:
17. 7 cm
Step-by-step explanation:
To find the length of the hypotenuse of a right triangle when the lengths of the legs are known, we can use the Pythagorean theorem:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Pythagorean Theorem}}\\\\c^2=a^2+b^2\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a$ and $b$ are the legs of the right triangle.}\\\phantom{ww}\bullet\;\textsf{$c$ is the hypotenuse (longest side) of the right triangle.}\\\end{array}}[/tex]
In this case, the legs measure:
Substitute the given values into the equation and solve for c:
[tex]c^2=5^2+17^2\\\\c^2=25+289\\\\c^2=314\\\\c=\sqrt{314}\\\\c=17.7200451466...\\\\c=17.7\; \sf cm\;(nearest\;tenth)[/tex]
Therefore, the length of the hypotenuse rounded to the nearest tenth is:
[tex]\LARGE\boxed{\boxed{17.7\; \sf cm}}[/tex]
