The height of an equilateral triangle equals I times the side length. Using I for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?

Answer 1

To find the height of an equilateral triangle, we can use the formula for the height $h$ in terms of the side length $s$:

$$h=\frac{\sqrt{3}}{2}s$$

In this case, the side length $s$ is given as 8 meters. Substituting this value into the formula gives:

$$h=\frac{\sqrt{3}}{2}\times 8$$

Now, calculate the height:

$$h=4\sqrt{3}$$

Since you mentioned using $I$ for the square root of 3, we can substitute $I$ in place of $\sqrt{3}$:

$$h=4I$$

Now, to find the approximate height, we need to evaluate $4I$. The approximate value of $\sqrt{3}$ is about $1.732$. Therefore:

$$h\approx 4\times 1.732=6.928$$

Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is:

$$\boxed{{\displaystyle 6.93}}\text{ meters}$$