We have a right triangle whose lengths are 26 inches and 36 inches.
We have that the largest side of a right triangle is the hypotenuse (c), and we can call the other side (one of the legs of the triangle) b. Then, using the Pythagorean Theorem, we have:
c = 36 inches.
b = 26 inches.
[tex]c^2=a^2+b^2[/tex]
We can solve this equation for a^2, subtracting b^2 to both sides of the equation:
[tex]c^2-b^2=a^2+b^2-b^2\Rightarrow c^2-b^2=a^2+0\Rightarrow a^2=c^2-b^2[/tex]
Then, we have:
[tex]a^2=36^2-26^2\Rightarrow\sqrt[]{a^2}=\sqrt[]{1296-676}\Rightarrow a=\sqrt[]{620}\Rightarrow a=24.899799[/tex]
Rounding this value to the nearest inch, we have that the value for a = 25 inches.
