An illustration shows a square pyramid with labeled parts. The left, front and right faces of the pyramid and base are visible. The back face is not visible. The back base edge is not visible but its position is indicated by a dashed line. The front base edge shows a length of 40 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. This dotted line shows a slant height of 25 feet.
Apply the Pythagorean Theorem to determine the height of the square pyramid, h . Round the answer to the nearest tenth.
To apply the Pythagorean theorem, we have a right triangle formed by the height line (h), the slant height (25 feet), and a portion of the base edge (unknown length). Let's call this unknown length x.
By the Pythagorean theorem, we have:
x^2 + h^2 = 25^2
Simplifying, we get:
x^2 + h^2 = 625
Since x is a portion of the base edge and we know that the front base edge has a length of 40 feet, we can subtract x from 40 to find the length of the back base edge. Let's call this length y.
y = 40 - x
Now we can use the fact that the base of the pyramid is a square, so the front and back base edges have the same length. Thus, we have:
y = x
Substituting y = 40 - x, we get:
40 - x = x
Simplifying, we find:
2x = 40
x = 20
Now we can substitute this value of x into the Pythagorean theorem equation to solve for h:
20^2 + h^2 = 625
400 + h^2 = 625
h^2 = 625 - 400
h^2 = 225
Taking the square root of both sides, we find:
h = 15
Therefore, the height of the square pyramid, h, is approximately 15 feet.
To apply the Pythagorean Theorem to determine the height of the square pyramid, we can use the following equation:
h^2 = l^2 - s^2
Where:
h = height of the pyramid
l = length of the base edge
s = slant height of the pyramid
From the information provided in the illustration, we know that:
l = 40 feet
s = 25 feet
Substituting these values into the equation, we have:
h^2 = 40^2 - 25^2
h^2 = 1600 - 625
h^2 = 975
To find the value of h, we need to take the square root of both sides of the equation:
h = √975
Using a calculator, we find that √975 is approximately equal to 31.3.
Therefore, the height of the square pyramid, h, rounded to the nearest tenth, is 31.3 feet.
To apply the Pythagorean Theorem in this case, we can use the relationship between the slant height, the height, and the base of the pyramid. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this illustration, the slant height of the pyramid is given as 25 feet, and the length of the base is given as 40 feet. We want to determine the height, which is labeled as "h".
To solve for the height, we can use the following equation:
h^2 + (1/2 * 40)^2 = 25^2
Here's how we derived the equation:
1. The base of the pyramid forms one side of the right triangle, so its length is used as one side of the equation.
2. The height of the pyramid forms another side of the triangle, so we use "h" as the other side.
3. The slant height of the pyramid is the hypotenuse of the right triangle, so we use 25 as the hypotenuse.
Now, let's solve the equation:
h^2 + 20^2 = 625
h^2 + 400 = 625
h^2 = 625 - 400
h^2 = 225
h = √225
h ≈ 15 feet
So, the height of the square pyramid is approximately 15 feet.