Question

the altitude of an equilateral triangle is 9 . how long is the length of a side of the equilateral triangle ?

Answer 1

the length of the side is 6√3 or 10.39

Step-by-step 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)

`\begin{gathered} x=9/\frac{\sqrt[]{3}}{2}\text{ =9}*\frac{2}{\sqrt[]{3}}\text{ } \\ \text{= 18/}\sqrt[]{3}\text{ = }\frac{18\sqrt[]{3}}{3} \\ =\text{ 6}\sqrt[]{3} \end{gathered}`

sin60 in decimal = 0.8660

x = 9/0.8660

x = 10.39

Hence, the length of the side is 6√3 or 10.39