Question

I don't understand this ​

Answer 1

Answer:

$m = 3 \sqrt{12}$

$n = 6$

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

${m}^{2} + {n}^{2} = {12}^{2}$

now lets put numbers on formula

${m}^{2} + {6}^{2} = {12}^{2}$

from this formula m=

$m = \sqrt{ {12}^{2} - {6}^{2} } = \sqrt{144 - 36} = \sqrt{108} = 3 \sqrt{12}$