Answer:
9.7 in
Step-by-step explanation:
The Pythagorean Theorem explains the relationship between the three sides of a right triangle. The square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the legs of a right triangle:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Pythagorean Theorem}}\\\\a^2+b^2=c^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]
From observation of the given right triangle, the hypotenuse measures 12.5 in, one of the legs measures 7.9 in, and the other leg is labelled 'x'.
Therefore:
To find the missing side length of the triangle (x), substitute the values into the equation and solve for x:
[tex]x^2+7.9^2=12.5^2\\\\x^2+62.41=156.25\\\\x^2=156.25-62.41\\\\x^2=93.84\\\\x=\sqrt{93.84}\\\\x=9.6871048306...\\\\x=9.7\; \sf in\;(nearest\;tenth)[/tex]
Therefore, the value of x is:
[tex]\LARGE\boxed{\boxed{x=9.7\; \sf in}}[/tex]
