Answer:
[tex]n=\dfrac{9}2[/tex]
[tex]m = 3\sqrt3[/tex]
Step-by-step explanation:
We can solve for sides n and m using the ratio of sides in a 30-60-90 triangle:
1 : [tex]\sqrt3[/tex] : 2
We are given the shorter leg to be:
[tex]\dfrac{3\sqrt3}{2}[/tex]
So, we can solve for the longer leg and the hypotenuse—n and m, respectively—by multiplying the shorter leg by [tex]\sqrt3[/tex] and 2:
[tex]n = \dfrac{3\sqrt3}{2} \cdot \sqrt3[/tex]
[tex]n = \dfrac{3\sqrt{3\cdot 3}}{2}[/tex]
[tex]n = \dfrac{3 \cdot 3}{2}[/tex]
[tex]\boxed{n=\dfrac{9}2}[/tex]
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[tex]m = \dfrac{3\sqrt3}{\not2} \,\cdot\! \not2[/tex]
[tex]\boxed{m = 3\sqrt3}[/tex]
