Answer:
Option 3 is correct.
Height of the equilateral triangle = 17.3 units
Step-by-step explanation:
In equilateral triangle each sides of equal length and an angle of 60 degree.
As per the statement: An equilateral triangle has sides of length 20.
To find the height of the equilateral triangle.
we can draw an altitude to one of the sides in order to divide the triangle into two equal triangles i.,e [tex]30^{\circ}-60^{\circ}-90^{\circ}[/tex].
Let sides of an equilateral triangle be b.
The side of an equilateral triangle is an hypotenuse of the [tex]30^{\circ}-60^{\circ}-90^{\circ}[/tex] triangle.
This [tex]30^{\circ}-60^{\circ}-90^{\circ}[/tex] triangle is a special triangle, we know that the sides are:
[tex]x , x\sqrt{3}, 2x[/tex]
Thus;
b = 2x
Divide both sides by 2 we get;
[tex]x = \frac{b}{2}[/tex]
Height of the equilateral triangle(h) is, [tex]\sqrt{3}x[/tex]
substitute the value of x and b = 20 units we get;
h = [tex]\frac{\sqrt{3}b}{2} = \frac{20\sqrt{3}}{2} = 10\sqrt{3} = 10 \times 1.732 = 17.32[/tex]
Therefore, the height of the equilateral triangle to the nearest tenth place is, 17.3 units
