We have a right triangle with hypotenuse 38 and leg 34.
We want to find the other leg.
We use the Pythagorean Theorem:
[tex]a^{2}+b^{2}=c^{2}[/tex]
[tex]\Rightarrow a^{2}+34^{2}=38^{2}[/tex]
[tex]\Rightarrow a^{2}+1156=1444[/tex]
[tex]\Rightarrow a^{2}=288[/tex]
[tex]\Rightarrow a=12\sqrt{2}\approx 17.0[/tex]
