The height of an equilateral triangle equals 3√/2 times the side length. Using 7/4 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?
Given that the height of an equilateral triangle is equal to 3√/2 times the side length, and using 7/4 as an approximation for √3:
Height = (3√/2) * Side Length
Height = (3 * 7/4) * 8
Height = (21/4) * 8
Height = 21 * 2
Height = 42
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters would be 42 meters.
To find the height of an equilateral triangle, we can use the given formula which states that the height is equal to 3√/2 times the side length.
Given that the side length of the triangle is 8 meters, we can substitute this value into the formula to find the height.
First, let's substitute the approximate value of square root of 3:
3√/2 ≈ 3 * (7/4) / 2
Simplifying the expression:
3 * (7/4) / 2 = 21/8
Now, we can find the height by multiplying the side length of 8 meters by 21/8:
Height = 8 * (21/8)
Simplifying the expression:
8 * (21/8) = 21 meters
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 21 meters.