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klasskru [66]
3 years ago
9

Triangle MNO is an equilateral triangle with sides measuring 16 square root of 3 units.

Mathematics
2 answers:
Olenka [21]3 years ago
6 0
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
8 \sqrt{3}  \times  \sqrt{3}  = 24
the height is 24 .
olga55 [171]3 years ago
4 0

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,

|NR|^2+|OR|^2=|ON|^2


From the diagram, |ON|=16\sqrt{3} units

and

|OR|=\frac{1}{2}\times 16\sqrt{3}


|OR|=8\sqrt{3} units.


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


|NR|^2+(8\sqrt{3})^2=(16\sqrt{3})^2

We evaluate to get,

|NR|^2+64(3)=256(3)


We group like terms to get,

|NR|^2=256(3)-64(3)


|NR|^2=3(256-64)


|NR|^2=3(192)


|NR|^2=576


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


NR=\sqrt{576}


NR=24


Therefore the height of the triangle is 24 units.











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