Apply the Pythagorean Theorem to determine the height of the square pyramid, h . Round the answer to the nearest tenth.
(1 point)
Responses
15.0 ft.
15.0 ft.
32.0 ft.
32.0 ft.
31.2 ft.
31.2 ft.
47.2 ft.
To determine the height of the square pyramid, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the two legs of the right triangle and c is the hypotenuse.
In this case, the legs of the right triangle are the height of the pyramid (h) and half of the base length (20 ft).
So, the equation becomes:
h^2 + 20^2 = 25^2
h^2 + 400 = 625
h^2 = 625 - 400
h^2 = 225
Taking the square root of both sides, we find:
h = √225
h = 15 ft
Therefore, the height of the square pyramid is 15.0 ft.
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
The diagonal of the base, segment BH, is given as 40 cm, and we are looking for the diagonal, segment BE.
Using the Pythagorean theorem, we have:
BE^2 = BH^2 + HE^2
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
Taking the square root of both sides, we find:
BE = √3536
BE ≈ 59.5 cm (rounded to the nearest tenth)
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.
To find the slant height of the paper cone, we can use the Pythagorean theorem.
Let the radius of the circle be r, which is half of the diameter. So, r = 13/2 = 6.5 cm.
The height of the cone is given as 6 cm.
Using the Pythagorean theorem, we have:
slant height^2 = height^2 + radius^2
slant height^2 = 6^2 + 6.5^2
slant height^2 = 36 + 42.25
slant height^2 = 78.25
Taking the square root of both sides, we find:
slant height ≈ √78.25
slant height ≈ 8.8 cm (rounded to the nearest tenth)
Therefore, the slant height of the paper cone should be approximately 8.8 cm.
To find the height of the tent, we can use the Pythagorean theorem.
Let h be the height of the tent.
The slant height of the tent is given as 13.5 m.
The length of each edge of the square base is given as 20 m.
Using the Pythagorean theorem, we have:
h^2 + (10)^2 = (13.5)^2
h^2 + 100 = 182.25
h^2 = 82.25
Taking the square root of both sides, we find:
h ≈ √82.25
h ≈ 9.1 m (rounded to the nearest tenth)
Therefore, the height of the tent is approximately 9.1 m.
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem.
Let the length of the ramp be denoted as r.
The length of the cage is given as 70 cm, the width is 35 cm, and the height is 50 cm.
Using the Pythagorean theorem, we have:
r^2 = length^2 + width^2 + height^2
r^2 = 70^2 + 35^2 + 50^2
r^2 = 4900 + 1225 + 2500
r^2 = 8625
Taking the square root of both sides, we find:
r ≈ √8625
r ≈ 92.9 cm (rounded to the nearest tenth)
Therefore, the ramp needs to be approximately 92.9 cm long to fit diagonally in the cage.
Without the specific measurements of the sides of the square pyramid, we cannot determine the height using the Pythagorean theorem.
The Pythagorean Theorem in Three Dimensions Quick Check
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Question
Use the image to answer the question.
A drawing shows a circle showing diameter below a sector of a circle showing slant height. A double-headed arrow crossing the center of the circle is labeled as d equals diameter. A dotted double-headed arrow is drawn from the top point of the sector of the circle to a point along the curved edge. The arrow is labeled as lower L equals slant height.
Chem Tech makes paper cones used to filter liquids in lab experiments. To make the paper cones, the company starts with the net of the shape, where the slant height is needed. The company wants the height of the cones to be 6 cm. If they make the diameter 13 cm, what must the slant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth.
(1 point)
Responses
8.8 cm
8.8 cm
14.3 cm
14.3 cm
11.5 cm
11.5 cm
2.5 cm
every single one is right trust i just did it holy crap i thought they were all wrong but nope there all right 100%
The Pythagorean Theorem in Three Dimensions Quick Check
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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. 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.
(1 point)
Responses
15.0 ft.
15.0 ft.
32.0 ft.
32.0 ft.
31.2 ft.
31.2 ft.
47.2 ft.
The Pythagorean Theorem in Three Dimensions Quick Check
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Question
Use the image to answer the question.
An illustration of a rectangular prism is shown with labeled parts. The left and back base edges are not visible but their positions are indicated by a dashed line. The 6 vertices are labeled A B C D E F and G. The base edge A B is labeled length. Base edge B C is labeled width. The perpendicular C D is labeled height. A dotted line crosses the rectangular base through the center to show diagonal B H. A dashed line extends up from the base indicating the left rear perpendicular E H. A dotted line crosses from the back top left vertex E to the front bottom right vertex B to show diagonal B E. This dotted line is labeled diagonal.
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)
Responses
54.4 cm
54.4 cm
46.6 cm
46.6 cm
51.2 cm
51.2 cm
59.5 cm