Respuesta :

M.N and O are 60 degree. And you have to know that 30 60 and 90 triangle. if 30 degrees opposite is measuring A , 60 is A square root 3 and the 90's opposite is being 2A. So 90 degree opposite is 16 square root 3 and 30 degree is being 8 square root 3 and 60 is
[tex]8 \sqrt{3} \times \sqrt{3} = 24[/tex]
the height is 24 .
kudzordzifrancis

Answer:

The height of the triangle is 24 units.

Step-by-step explanation:

The height of the given triangle is NR

Using the Pythagorean Theorem,

[tex]|NR|^2+|OR|^2=|ON|^2[/tex]


From the diagram, [tex]|ON|=16\sqrt{3}[/tex] units

and

[tex]|OR|=\frac{1}{2}\times 16\sqrt{3}[/tex]


[tex]|OR|=8\sqrt{3}[/tex] units.


We substitute all these values into the above formula to get,


[tex]|NR|^2+(8\sqrt{3})^2=(16\sqrt{3})^2[/tex]

We evaluate to get,

[tex]|NR|^2+64(3)=256(3)[/tex]


We group like terms to get,

[tex]|NR|^2=256(3)-64(3)[/tex]


[tex]|NR|^2=3(256-64)[/tex]


[tex]|NR|^2=3(192)[/tex]


[tex]|NR|^2=576[/tex]


We take the positive square root of both sides to get,


[tex]NR=\sqrt{576}[/tex]


[tex]NR=24[/tex]


Therefore the height of the triangle is 24 units.











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