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