Question

using 7 over 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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the height of an equilateral triangle with a side length of 8 meters, we can use the formula:

Height = (square root of 3) * (side length) / 2

Substituting square root of 3 as 7 over 4 and the side length as 8, we have:

Height = (7/4) * 8 / 2
= (7/4) * 4
= 7

Therefore, the approximate height of the equilateral triangle is 7 meters.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the height of an equilateral triangle, we can use the formula h = (√3/2) * s, where h represents the height and s represents the length of the side.

Given that the side length of the equilateral triangle is 8 meters, we can substitute s = 8 into the formula:

h = (√3/2) * 8

Now let's calculate the value of (√3/2) using 7 over 4 as an approximation for the square root of 3:

(√3/2) ≈ (√7/4)

Substituting this approximation, we have:

h ≈ (√7/4) * 8

Let's simplify this expression:

h ≈ (8√7)/4

h ≈ 2√7

So, the approximate height of the equilateral triangle with a side length of 8 meters is 2√7 meters.

Answer 3

[AI-generated answer — Explain Bot]

To find the approximate height of an equilateral triangle with a side length of 8 meters, we can use the formula:

Height = (Square Root of 3) * (side length) / 2.

Given that the square root of 3 is approximately 1.732 (using 7 over 4 as an approximation), and the side length is 8 meters, we can substitute these values into the formula:

Height = (1.732) * (8) / 2.

Simplifying the expression, we get:

Height = 13.856 / 2.

Calculating the final result:

Height ≈ 6.928 meters.

Hence, the approximate height of an equilateral triangle with a side length of 8 meters is approximately 6.928 meters.