Answer:
[tex]m = 3 \sqrt{12} [/tex]
[tex]n = 6[/tex]
Step-by-step explanation:
n=1/2 of 12 according to the rule:
right triangle the side opposite the 30 degree angle is half the length of the hypotenuse.
so n=12/2=6
and now we will need Pythagorean theorem : the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
so
[tex] {m}^{2} + {n}^{2} = {12}^{2} [/tex]
now lets put numbers on formula
[tex] {m}^{2} + {6}^{2} = {12}^{2} [/tex]
from this formula m=
[tex]m = \sqrt{ {12}^{2} - {6}^{2} } = \sqrt{144 - 36} = \sqrt{108} = 3 \sqrt{12} [/tex]
