use the pythagorean theorem to find the distance between (7,8) and (3,2). Round your answer to the nearest hundredth
The distance between two points in a plane can be found using the Pythagorean theorem, which states that in a right triangle, the square 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, the two points are (7,8) and (3,2), representing the coordinates of two vertices of a right triangle. The sides of the triangle are the horizontal distance between the points (called the base or x-coordinate difference) and the vertical distance between the points (called the height or y-coordinate difference).
The x-coordinate difference between (7,8) and (3,2) is 7 - 3 = 4.
The y-coordinate difference between (7,8) and (3,2) is 8 - 2 = 6.
Using the Pythagorean theorem, we can find the length of the hypotenuse (the distance between the two points) by taking the square root of the sum of the squares of the base and height.
Distance = √(base^2 + height^2)
Distance = √(4^2 + 6^2)
Distance = √(16 + 36)
Distance = √52
Distance ≈ 7.21 (rounded to the nearest hundredth)
Therefore, the distance between (7,8) and (3,2) is approximately 7.21 units.
find the slant height of a square pyramid. 16 is the bas, while 15 is the height
To find the slant height of a square pyramid, we can use the Pythagorean theorem. In a square pyramid, the slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half of the base length.
Given that the base length of the square pyramid is 16 units and the height is 15 units, we can find the slant height.
The half of the base length is 16 / 2 = 8 units.
Using the Pythagorean theorem, we can find the slant height:
Slant height = √(height^2 + (base/2)^2)
Slant height = √(15^2 + 8^2)
Slant height = √(225 + 64)
Slant height = √289
Slant height = 17
Therefore, the slant height of the square pyramid is 17 units.
find the length of the diagonal of the prism. the height is 12, the length is 4, and the width is 3
To find the length of the diagonal of a rectangular prism, we can use the Pythagorean theorem. In a rectangular prism, the diagonal is the hypotenuse of a right triangle formed by the height, length, and width.
Given that the height of the prism is 12, the length is 4, and the width is 3, we can find the length of the diagonal.
Using the Pythagorean theorem:
Diagonal = √(height^2 + length^2 + width^2)
Diagonal = √(12^2 + 4^2 + 3^2)
Diagonal = √(144 + 16 + 9)
Diagonal = √169
Diagonal = 13
Therefore, the length of the diagonal of the prism is 13.
The Great Pyramid of Giza in Egypt has a square base with edge length of 230.5 m and a slant height of 180.2 m. Find the height of the pyramid. Round to the nearest tenth.
To find the height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height, half of the base length, and the slant height.
Given that the base length is 230.5 m and the slant height is 180.2 m, we can find the height.
Half of the base length is 230.5 / 2 = 115.25 m.
Using the Pythagorean theorem:
Slant height = √(height^2 + (base/2)^2)
180.2 = √(height^2 + (115.25)^2)
Squaring both sides:
180.2^2 = height^2 + 115.25^2
32544.04 = height^2 + 13286.5625
height^2 = 32544.04 - 13286.5625
height^2 = 19257.4775
Taking the square root of both sides:
height = √19257.4775
height ≈ 138.8
Therefore, the height of the pyramid is approximately 138.8 m rounded to the nearest tenth.
whats 138.526 rounded to the nearest tenth
138.526 rounded to the nearest tenth is 138.5.
To find the distance between the points (7, 8) and (3, 2) using the Pythagorean theorem, follow these steps:
Step 1: Identify the coordinates of the two points:
Point 1: (7, 8)
Point 2: (3, 2)
Step 2: Determine the difference in x-coordinates and y-coordinates:
Δx = x2 - x1 = 3 - 7 = -4
Δy = y2 - y1 = 2 - 8 = -6
Step 3: Square the differences:
(Δx)^2 = (-4)^2 = 16
(Δy)^2 = (-6)^2 = 36
Step 4: Apply the Pythagorean theorem formula:
Distance = √((Δx)^2 + (Δy)^2)
Distance = √(16 + 36) = √52 ≈ 7.21
Therefore, the distance between the points (7, 8) and (3, 2) is approximately 7.21 units when rounded to the nearest hundredth.