Answer :

iGreen
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.