Answer:
[tex]m=\dfrac{9\sqrt3}{2}[/tex]
[tex]n=\dfrac{9}{2}[/tex]
Step-by-step explanation:
The ratio of side lengths in a 30-60-90 triangle is:
1 : [tex]\sqrt3[/tex] : 2
We are given the hypotenuse (longest side) and asked to solve for [tex]m[/tex] and [tex]n[/tex], which are the long and short legs, respectively.
We can solve for these sides by multiplying by the ratio:
[tex]\rm hypotenuse \times \dfrac{long\ leg}{hypotenuse} = long\ leg[/tex]
↓ plugging in the known values
[tex]m = 9 \times \dfrac{\sqrt3}{2} = \boxed{\dfrac{9\sqrt3}{2}}[/tex]
__
[tex]\rm hypotenuse \times \dfrac{short\ leg}{hypotenuse} = short\ leg[/tex]
↓ plugging in the known values
[tex]n = 9 \times \dfrac{1}{2} = \boxed{\dfrac{9}{2}}[/tex]
