Use Cosine to find 'n'.
[tex]\sf~Cosine=\dfrac{Adjacent}{Hypotenuse}[/tex]
Plug in what we know:
[tex]\sf~cos(45^o)=\dfrac{n}{6\sqrt{2}}[/tex]
Simplify the cosine of 45 degrees and 6 times the square root of 2:
[tex]\sf~0.707106781=\dfrac{n}{8.48528137}[/tex]
Multiply 8.48528137 to both sides:
[tex]\sf~n=6[/tex]
Now that we have 'n', we can use the Pythagorean Theorem to find 'm'.
[tex]\sf~a^2+b^2=c^2[/tex]
Where 'a' and 'b' are the two legs of the right triangle and 'c' is the hypotenuse.
Plug in what we know:
[tex]\sf~a^2+6^2=(6\sqrt2)^2[/tex]
Simplify the exponents:
[tex]\sf~a^2+36=72[/tex]
Subtract 36 to both sides:
[tex]\sf~a^2=36[/tex]
Find the square root of both sides:
[tex]\sf~a=\sqrt{36}[/tex]
[tex]\sf~a=6[/tex]
So 'n' and 'm' are both equal to 6.
