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A rectangular box is 8 inches in length, 3 inches in width, and 5 inches in height.
The figure shows a rectangular box of length 8 inches, width 3 inches, and height 5 inches. The diagonal of this rectangular box is the hypotenuse of a right triangle and the height of the rectangular box is the height of the triangle.
Suppose the three-dimensional diagonal is also the hypotenuse of a right triangle. If a vertical edge is one of the legs of that right triangle, what is the length of the second leg? Round your answer to the nearest tenth of an inch. Show all of your work.
Determine the length of the three-dimensional diagonal. Round your answer to the nearest tenth of an inch. Show all of your work.
The "second leg" of the right-angled triangle is the diagonal of the base of the box
let that length be x
x^2 = 8^2 + 3^ = 73
Let the length of the 3-D diagonal be d
d^2 = x^2 + 5^2
= 73 + 25 = ...
I will let you finish this
To find the length of the three-dimensional diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of the rectangular box (8 inches) will be one of the legs of the triangle, and the height of the rectangular box (5 inches) will be the other leg.
Let's calculate the length of the three-dimensional diagonal:
Step 1: Square the length of the rectangular box's length and height.
Length squared = 8^2 = 64
Height squared = 5^2 = 25
Step 2: Find the sum of the squares.
64 + 25 = 89
Step 3: Take the square root of the sum to find the length of the three-dimensional diagonal.
Square root of 89 = 9.43 inches (rounded to the nearest tenth)
So, the length of the three-dimensional diagonal is approximately 9.43 inches.
To find the length of the three-dimensional diagonal of the rectangular box, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can consider the length, width, and height of the rectangular box as the three sides of a right triangle. Let's label the length as L = 8 inches, the width as W = 3 inches, and the height as H = 5 inches.
First, find the square of each side:
L^2 = 8^2 = 64
W^2 = 3^2 = 9
H^2 = 5^2 = 25
Now, add the squares of the two shorter sides:
9 + 25 = 34
Finally, find the square root of the sum to get the length of the three-dimensional diagonal:
√34 ≈ 5.8 inches
So, the length of the three-dimensional diagonal is approximately 5.8 inches.
Now let's find the length of the second leg of the right triangle formed by the three-dimensional diagonal and a vertical edge of the rectangular box.
We can use the Pythagorean theorem again. Let's label the second leg as X.
Using the same method as above, we can set up the following equation:
X^2 + H^2 = 5.8^2
Substituting the value of H and simplifying the equation:
X^2 + 25 = 33.64
Rearranging the equation to solve for X:
X^2 = 33.64 - 25
X^2 = 8.64
Taking the square root of both sides:
X = √8.64 ≈ 2.9 inches
So, the length of the second leg of the right triangle is approximately 2.9 inches.
I am confused this is the question
The volume of a rectangular prism is 288 cubic inches. The length of the rectangular prism is 0.36 inches and the width is 8 inches. What is the height of the rectangular prism?