the length of the side is 6√3 or 10.39
Explanation:altitude = 9
An equilateral triangle has all sides and angle equal
The measure of each of the angle is 60 degrees
A half diagram of the triangle:
Let the length of the side = x
opposite = atitude = 9
hypotenuse =x
angle = 60 degrees
using sine ratio:
sin 60 = opposite/hypotense
sin 60 = 9/x
cross multiply:
xsin60 = 9
x = 9/sin60
In rational form, sin60 = √3/2
x = 9/(√3/2)
[tex]\begin{gathered} x=9\div\frac{\sqrt[]{3}}{2}\text{ =9}\times\frac{2}{\sqrt[]{3}}\text{ } \\ \text{= 18/}\sqrt[]{3}\text{ = }\frac{18\sqrt[]{3}}{3} \\ =\text{ 6}\sqrt[]{3} \end{gathered}[/tex]sin60 in decimal = 0.8660
x = 9/0.8660
x = 10.39
Hence, the length of the side is 6√3 or 10.39
