The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)
The height of an equilateral triangle is equal to 3√2 times the side length.
Given that the side length is 8 meters, we can substitute this value into the equation:
Height = 3√2 * 8
Using 74 as the approximate value for the square root of 3, we can substitute this into the equation as well:
Height = 3 * 74 * 8
Calculating this expression gives us:
Height = 3 * 74 * 8 = 1776
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 1776 meters.
The diagonal of a square equals 2–√ times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?(1 point)
The diagonal of a square is equal to 2–√ times the side length.
Given that the side length of the square park is 700 feet, we can substitute this value into the equation:
Diagonal = 2–√ * 700
Using 1.4 as the approximate value for the square root of 2, we can substitute this into the equation as well:
Diagonal = 2 * 1.4 * 700
Calculating this expression gives us:
Diagonal = 2 * 1.4 * 700 = 1960
Therefore, the approximate length from one corner to an opposite corner of a square park with a side length of 700 feet is 1960 feet.
The diagonal of a square equals √2 times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?(1 point)
The diagonal of a square is equal to √2 times the side length.
Given that the side length of the square park is 700 feet, we can substitute this value into the equation:
Diagonal = √2 * 700
Using 1.4 as the approximate value for the square root of 2, we can substitute this into the equation as well:
Diagonal = 1.4 * 700
Calculating this expression gives us:
Diagonal = 1.4 * 700 = 980
Therefore, the approximate length from one corner to an opposite corner of a square park with a side length of 700 feet is 980 feet.
Using a number line, what whole number and rational number to the nearest half is √40 between?(1 point)
To determine the whole number and rational number to the nearest half that √40 is between, we can find the two closest integers to √40 on a number line.
First, we can find the closest whole number to √40, which is 6. Since 40 is closer to 36 (6^2) than 49 (7^2).
Next, we can find the closest rational number to √40. To do this, we can consider the rational numbers closest to √40. The rational number 6.5 (or 13/2) is greater than √40, and the rational number 6 (or 12/2) is less than √40.
Therefore, √40 is between 6 and 6.5 (or 12/2 and 13/2) on the number line.
Using a number line, what whole number and rational number to the nearest half is √58 between?
To determine the whole number and rational number to the nearest half that √58 is between, we can find the two closest integers to √58 on a number line.
First, we can estimate the value of √58. Since 58 is between the perfect squares of 49 (7^2) and 64 (8^2), we know that √58 is between 7 and 8.
Next, we can find the closest rational number to √58. To do this, we can consider the rational numbers closest to √58. The rational number 7.5 (or 15/2) is greater than √58, and the rational number 7 (or 14/2) is less than √58.
Therefore, √58 is between 7 and 7.5 (or 14/2 and 15/2) on the number line.
To find the height of an equilateral triangle, we can use the formula: height = side length * (√3) / 2.
Given that the side length is 8 meters, we can substitute it into the formula: height = 8 * (√3) / 2.
Now, we need to use the given value of √3, which is 74. Plugging it into the formula: height = 8 * (74) / 2.
Simplifying the expression: height = 4 * 74.
Calculating the height: height = 296 meters.
Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is 296 meters.