Apply the Pythagorean Theorem to determine the height of the square pyramid, h . Round the answer to the nearest tenth.
The answers to the quick check are
15.0 ft
59.5 cm
8.8 cm
9.1 m
92.9 cm
Thanks so much! Anonymous is %100 correct
To apply the Pythagorean Theorem to determine the height of the square pyramid, we need to have the lengths of the base and the slant height.
The Pythagorean Theorem states that in a right-angled 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.
For a square pyramid, let's denote the length of the base as b and the slant height as s. The height of the pyramid can be calculated by substituting the known values into the Pythagorean Theorem formula and solving for h:
h^2 = s^2 - (b/2)^2
To determine the height of the square pyramid, you will need to know the slant height and the length of the base.
To apply the Pythagorean Theorem to determine the height of a square pyramid, we need to determine the length of the slant height of the pyramid's lateral face. Here are the steps:
1. Identify the given information: We need to know the lengths of the base edges of the square pyramid. Let's denote the length of each base edge as "s".
2. Calculate the square of the base diagonal: The base diagonal is the line segment connecting any two opposite corners of the base square. The length of the base diagonal can be found using the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the base diagonal is the hypotenuse, while the two sides are the base edges (s). The formula can be expressed as: diagonal^2 = s^2 + s^2
Simplifying the equation, we get: diagonal^2 = 2s^2
3. Find the square of the slant height: The slant height of the lateral face of a square pyramid is the height of each triangular face. It can be calculated by using half the length of the base diagonal and the height of the pyramid (h). Let's denote the slant height as "l".
The Pythagorean Theorem can be applied again to find the square of the slant height:
l^2 = diagonal^2 + h^2
Substituting the value of diagonal^2 from step 2, we get:
l^2 = 2s^2 + h^2
4. Solve for the square of the slant height. Let's assume we know the value of "s". Solve the equation obtained in step 3 to find the square of the slant height, l^2.
5. Once you have the square of the slant height (l^2), take the square root of it to find the actual slant height of the pyramid (l).
6. Calculate the height of the square pyramid, h: Subtract the slant height (l) from the apex (the top point of the pyramid), which is also the perpendicular distance from the apex to the base.
To apply the Pythagorean Theorem to determine the height of a square pyramid, you will need the lengths of the base and one of the slant heights of the pyramid.
Let's denote the length of one side of the square base as b, and the slant height as s.
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 case, we can define a right triangle by drawing the height of the pyramid from the apex perpendicular to the base. The height, h, will be one side of the triangle, while half the length of the base, b/2, will be the other side.
The slant height, s, will be the hypotenuse of this right triangle.
Therefore, we can write the equation using the Pythagorean Theorem:
s^2 = (b/2)^2 + h^2
To solve for h, we rearrange the equation:
h^2 = s^2 - (b/2)^2
h = √(s^2 - (b/2)^2)
Make sure to substitute the given values of s and b into this equation. Then, use a calculator to evaluate the square root. Finally, round the answer to the nearest tenth.
Apply the Pythagorean Theorem to determine the height of the square pyramid, h . Round the answer to the nearest tenth.
(1 point)
Responses
31.2 ft.
31.2 ft.
15.0 ft.
15.0 ft.
47.2 ft.
47.2 ft.
32.0 ft.
I'm sorry, but I'm unable to solve this question without further information and specific values for the base length and slant height. Please provide the necessary values to calculate the height of the square pyramid accurately.
The length of the prism is 32 cm, the width is 24 cm, the height is 44 cm, and the length of the diagonal of the base, segment BH , is 40 cm. Find the length of the diagonal of the rectangular prism, segment BE . Round the answer to the nearest tenth.
(1 point)
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean Theorem.
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 case, segment BE is the hypotenuse of a right triangle formed by segments BH, HE, and BE.
We know the length of segment BH (40 cm) and the height of the prism (44 cm). Let's denote the length of segment BE as x.
Using the Pythagorean Theorem, we can set up the following equation:
BE^2 = BH^2 + HE^2
x^2 = 40^2 + 44^2
x^2 = 1600 + 1936
x^2 = 3536
Taking the square root of both sides, we get:
x ≈ 59.4 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.4 cm (rounded to the nearest tenth).