The area of a square garden is 400 m 2 . How long is the diagonal? Round your answer to the hundredths place. (1 point)
28.28 m
18 m
20 m
6.32 m
To find the length of the diagonal of the square garden, we can use the Pythagorean Theorem.
Let's call the side length of the square garden "x". Since the area of the square is given as 400 m^2, we can set up the equation:
x^2 = 400
Taking the square root of both sides, we find:
x = √400
x = 20
So the side length of the square garden is 20 m.
To find the diagonal, we can use the formula for the diagonal of a square, which is the square root of 2 times the side length:
diagonal = √2 * x
diagonal = √2 * 20
diagonal = 28.28
Thus, the length of the diagonal of the square garden is 28.28 m. Therefore, the correct answer is 28.28 m.
To find the distance the supplies travel from one end of the conveyor belt to the other, we can use trigonometry.
Let's call the distance the supplies travel "d".
The supplies travel along the hypotenuse of a right triangle, where the height from the ground to the second floor is the opposite side and the distance along the ground is the adjacent side. The angle between the ground and the hypotenuse is 60°.
Using the trigonometric function cosine, we can set up the equation:
cos(60°) = Adjacent / Hypotenuse
Since cos(60°) = 1/2, the equation becomes:
1/2 = Adjacent / Hypotenuse
The height from the ground to the second floor is 14 feet, which is the opposite side of the triangle. Therefore, we can set up another equation:
Opposite = 14 feet
We can use the equation Opposite = Hypotenuse * sin(angle) to solve for the hypotenuse:
14 = Hypotenuse * sin(60°)
Since sin(60°) = sqrt(3)/2, the equation becomes:
14 = Hypotenuse * sqrt(3)/2
Multiplying both sides by 2/sqrt(3), we get:
Hypotenuse = 14 * 2/sqrt(3)
Hypotenuse = (28/sqrt(3)) feet
The supplies travel along the hypotenuse, which is also the distance they travel from one end of the conveyor belt to the other. So, the distance is:
d = 28/sqrt(3) feet
d ≈ 16.17 feet
Therefore, the supplies travel approximately 16.17 feet from one end of the conveyor belt to the other.
To find the value of angle "x" in the right triangle, we can use the trigonometric function sine.
Let's call the angle opposite the leg of length 25 units "y", and the angle opposite the hypotenuse of length 40 units "x".
We know that sine is defined as Opposite / Hypotenuse.
So, for angle "x":
sin(x) = Opposite / Hypotenuse
sin(x) = 25/40
To find the value of "x", we need to take the inverse sine (also known as arcsine) of both sides:
x = arcsin(25/40)
Using a calculator, we can find the value of arcsin(25/40) ≈ 0.6435 radians.
To convert this to degrees, we can multiply by 180/π:
x ≈ 0.6435 * (180/π) ≈ 36.87 degrees
Therefore, the value of angle "x" is approximately 36.87 degrees.
To find the length of leg "x" in the right triangle, we can use the trigonometric function cosine.
Let's call the angle between leg "x" and the hypotenuse "y". Given that the hypotenuse is 4.1 m long and the angle "y" is 40°:
cos(y) = Adjacent / Hypotenuse
cos(40°) = x / 4.1
Using a calculator, we can find the value of cos(40°) ≈ 0.7660.
Now we can solve for "x":
0.7660 = x / 4.1
Multiply both sides by 4.1:
3.1466 ≈ x
Rounding to the nearest hundredth of a meter, the length of leg "x" is approximately 3.15 m.
To find the length of the hypotenuse "x" in the right triangle, we can use the trigonometric function cosine.
Let's call the angle between the leg of length 48 units and the hypotenuse "y". Given that the angle "y" is 37 degrees:
cos(y) = Adjacent / Hypotenuse
cos(37°) = 48 / x
Using a calculator, we can find the value of cos(37°) ≈ 0.7986.
Now we can solve for "x":
0.7986 = 48 / x
Multiply both sides by x:
0.7986x = 48
Divide both sides by 0.7986:
x = 48 / 0.7986 ≈ 60.086
Rounding to the nearest tenth, the length of the hypotenuse "x" is approximately 60.1 units.
To find the length of leg "x" in the right triangle, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two legs (a and b):
c^2 = a^2 + b^2
In this case, we know that the length of the hypotenuse (c) is 27, and one of the leg lengths (a) is 16.
Plugging in the known values into the formula, we get:
27^2 = 16^2 + x^2
Simplifying, we have:
729 = 256 + x^2
Now, subtract 256 from both sides:
473 = x^2
To solve for x, we can take the square root of both sides:
x = √473
Using a calculator, we find that √473 ≈ 21.7485
So, the length of leg "x" is approximately 21.75.