step by step bot not the reguarl ai please answer this Use the image to answer the question.
An illustration shows a three dimensional rectangular prism with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides is labeled h. A right angle is indicated where that edge meets the front base edge. The front base edge is labeled l. A right angle is indicated where that edge meets the right base edge. The right base edge is labeled w. Two dotted lines extend from the vertex at the back right side of the prism through the interior. The first dotted line extends up to the vertex at the front left side and is labeled d. The second dotted line extends diagonally across the base to the vertex at the front left side where the perpendicular height line meets the base edge and is labeled x.
Given l=30 in. , w=20 in. , h=18 in. , and x=36.1 in. , find the length of d . Round the answer to the nearest tenth.
To find the length of d, we can use the Pythagorean Theorem because we have a right triangle formed by d, x, and the height of the prism.
1. Identify the right triangle formed by d, x, and the height of the prism.
2. Apply the Pythagorean Theorem to find the length of d:
d^2 = x^2 + h^2
3. Substitute the given values:
d^2 = (36.1 in.)^2 + (18 in.)^2
4. Calculate:
d^2 = 1303.21 in^2 + 324 in^2
d^2 = 1627.21 in^2
5. Take the square root of both sides to solve for d:
d = √(1627.21 in^2)
6. Round the answer to the nearest tenth:
d ≈ 40.3 in.
Therefore, the length of d is approximately 40.3 inches.
To find the length of "d", we can use the Pythagorean theorem, which 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.
In this case, we have a right-angled triangle formed by the side lengths "d", "h", and "x". The side lengths "h" and "x" are known, so we can substitute them into the formula and solve for "d".
The Pythagorean theorem can be written as:
d^2 = h^2 + x^2
Substituting in the given values:
d^2 = 18^2 + 36.1^2
Calculating:
d^2 = 324 + 1303.21
d^2 = 1627.21
To find the value of "d", we can take the square root of both sides:
d = sqrt(1627.21)
Calculating:
d ≈ 40.3 in.
Therefore, the length of "d" is approximately 40.3 inches.
To find the value of d, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, d is the hypotenuse, and the other two sides are x and l.
Using the Pythagorean theorem, we can write the following equation:
d² = x² + l²
Substituting the given values:
d² = (36.1 in)² + (30 in)²
d² = 1303.21 in² + 900 in²
d² = 2203.21 in²
To find the value of d, we take the square root of both sides:
d = √(2203.21 in²)
Calculating this, we find:
d ≈ 46.9 in
Therefore, the length of d, rounded to the nearest tenth, is approximately 46.9 inches.
step by step bot not the reguarl ai please answer this Use the image to answer the question.Use the image to answer the question.
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, but its position is indicated by a dashed line. The back base edge is not visible, but its position is indicated by a dashed line. The left base edge is labeled a. The back left lateral edge is labeled e. 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 and is labeled r. 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. The dotted slant height line is labeled s.
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.
To find the length of h, we first need to find the length of r. We can use the Pythagorean theorem to find r because we have a right triangle formed by h, r, and s.
1. Identify the right triangle formed by h, r, and s.
2. Apply the Pythagorean theorem to find the length of r:
r^2 = s^2 - h^2
3. Substitute the given values:
r^2 = (24 in.)^2 - h^2
4. Calculate:
r^2 = 576 in^2 - h^2
5. To find h, we need to know the value of r. However, the length of r is not given in the problem.
6. Therefore, we cannot solve for the length of h without the value of r.
Use the image to answer the question.
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, but its position is indicated by a dashed line. The back base edge is not visible, but its position is indicated by a dashed line. The left base edge is labeled a. The back left lateral edge is labeled e. 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 and is labeled r. 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. The dotted slant height line is labeled s.
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.
(1 point)
The height of the square pyramid is
in.
To find the height of the pyramid, h, we can use the Pythagorean theorem and the given values of e and s.
1. Identify the right triangle formed by h, r, and s.
2. Since we don't have the value of r, we first need to find it. Let's focus on finding r.
3. We can see that r is the height of the right triangle formed by h, r, and the slant height s.
4. Apply the Pythagorean theorem to this right triangle:
r^2 = s^2 - h^2
5. Substitute the given values:
r^2 = (24 in)^2 - h^2
6. Simplify:
r^2 = 576 in^2 - h^2
7. To solve for r, we need to know the value of h. However, we also need to know the value of r to find h.
8. Unfortunately, without the value of either h or r, we cannot solve for the height of the pyramid.
Therefore, without additional information, we cannot determine the height of the square pyramid.
h is 8
Thank you for providing the value of h. With h = 8 inches, we can now find the length of r and then determine the height of the pyramid.
1. We will use the Pythagorean theorem to find the length of r. From the right triangle formed by h, r, and s, we have:
r^2 = s^2 - h^2
r^2 = (24 in)^2 - (8 in)^2
r^2 = 576 in^2 - 64 in^2
r^2 = 512 in^2
r ≈ √512 in
r ≈ 22.63 in
2. Now that we have the length of r, we can find the height of the pyramid. The height of the pyramid is the perpendicular distance from the apex to the base. This height is equal to h.
Thus, the height of the square pyramid is 8 inches.
Therefore, the height of the square pyramid is 8 inches.
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.