To determine if a triangle is a right triangle, we can use the Pythagorean Theorem. According to the theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (hypotenuse).
Let's calculate the squares of the lengths of the sides:
60^2 = 3600
75^2 = 5625
45^2 = 2025
Now, let's arrange the side lengths in ascending order: 2025, 3600, 5625.
If the sum of the squares of the two smaller side lengths equals the square of the longest side length, then the triangle is a right triangle.
Is 2025 + 3600 = 5625?
Yes, 2025 + 3600 = 5625.
Therefore, since the sum of the squares of the two shorter sides is equal to the square of the longest side, the given triangle with sides measuring 60, 75, and 45 is indeed a right triangle.
If a triangle has sides measuring 60, 75, and 45, is it a right triangle?
15 answers
if triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.
To determine if a triangle is a right triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (hypotenuse).
Let's calculate the squares of the lengths of the sides:
50^2 = 2500
40^2 = 1600
32^2 = 1024
Now, let's arrange the side lengths in ascending order: 1024, 1600, 2500.
If the sum of the squares of the two smaller side lengths equals the square of the longest side length, then the triangle is a right triangle.
Is 1024 + 1600 = 2500?
Yes, 1024 + 1600 = 2624.
Therefore, since the sum of the squares of the two shorter sides is not equal to the square of the longest side, the given triangle with sides measuring 50, 40, and 32 is not a right triangle.
Answer: 0
Let's calculate the squares of the lengths of the sides:
50^2 = 2500
40^2 = 1600
32^2 = 1024
Now, let's arrange the side lengths in ascending order: 1024, 1600, 2500.
If the sum of the squares of the two smaller side lengths equals the square of the longest side length, then the triangle is a right triangle.
Is 1024 + 1600 = 2500?
Yes, 1024 + 1600 = 2624.
Therefore, since the sum of the squares of the two shorter sides is not equal to the square of the longest side, the given triangle with sides measuring 50, 40, and 32 is not a right triangle.
Answer: 0
Apply the Pythagorean Theorem to find the length between the two points (3,2) and (7,8) . Round your answer to the nearest hundredth.
To find the length between two points (x1, y1) and (x2, y2) using the Pythagorean Theorem, we can use the formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are (3, 2) and (7, 8). Substituting the values into the formula:
distance = √((7 - 3)^2 + (8 - 2)^2)
distance = √(4^2 + 6^2)
distance = √(16 + 36)
distance = √52
distance ≈ 7.21
So, the length between the two points (3, 2) and (7, 8) is approximately 7.21 rounded to the nearest hundredth.
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are (3, 2) and (7, 8). Substituting the values into the formula:
distance = √((7 - 3)^2 + (8 - 2)^2)
distance = √(4^2 + 6^2)
distance = √(16 + 36)
distance = √52
distance ≈ 7.21
So, the length between the two points (3, 2) and (7, 8) is approximately 7.21 rounded to the nearest hundredth.
Apply the Pythagorean Theorem to find the length between the two points (3,2) and (7,8) on a coordinate plane . Round your answer to the nearest hundredth.
To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, we can use the Pythagorean theorem:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are (3, 2) and (7, 8). Substituting the values into the formula:
distance = √((7 - 3)^2 + (8 - 2)^2)
distance = √(4^2 + 6^2)
distance = √(16 + 36)
distance = √52
distance ≈ 7.21
Therefore, the distance between the points (3, 2) and (7, 8) on a coordinate plane is approximately 7.21, rounded to the nearest hundredth.
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are (3, 2) and (7, 8). Substituting the values into the formula:
distance = √((7 - 3)^2 + (8 - 2)^2)
distance = √(4^2 + 6^2)
distance = √(16 + 36)
distance = √52
distance ≈ 7.21
Therefore, the distance between the points (3, 2) and (7, 8) on a coordinate plane is approximately 7.21, rounded to the nearest hundredth.
find the slant height of a pyramid with a base edge of 16 and a height of 15
To find the slant height of a pyramid, we can use the Pythagorean theorem. The slant height, denoted as "l", is the hypotenuse of a right triangle formed by the height of the pyramid (h) and half the length of the base edge (b/2).
In this case, the height of the pyramid (h) is 15 and the base edge (b) is 16.
We can find the slant height (l) using the formula:
l = √(h^2 + (b/2)^2)
Substituting the values:
l = √(15^2 + (16/2)^2)
l = √(225 + 8^2)
l = √(225 + 64)
l = √289
l = 17
Therefore, the slant height of the pyramid with a base edge of 16 and a height of 15 is 17 units.
In this case, the height of the pyramid (h) is 15 and the base edge (b) is 16.
We can find the slant height (l) using the formula:
l = √(h^2 + (b/2)^2)
Substituting the values:
l = √(15^2 + (16/2)^2)
l = √(225 + 8^2)
l = √(225 + 64)
l = √289
l = 17
Therefore, the slant height of the pyramid with a base edge of 16 and a height of 15 is 17 units.
he 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 the answer to the nearest tenth.(1 point)
To find the height of the pyramid, we can use the Pythagorean theorem. The height of the pyramid (h) forms a right triangle with half the length of the base edge (b/2) and the slant height (l).
In this case, the base edge (b) is 230.5 m and the slant height (l) is 180.2 m.
We can find the height (h) using the formula:
h = √(l^2 - (b/2)^2)
Substituting the values:
h = √(180.2^2 - (230.5/2)^2)
h = √(32544.04 - 26519.0125)
h = √(6037.0275)
h ≈ 77.7
Therefore, the height of the pyramid is approximately 77.7 meters, rounded to the nearest tenth.
In this case, the base edge (b) is 230.5 m and the slant height (l) is 180.2 m.
We can find the height (h) using the formula:
h = √(l^2 - (b/2)^2)
Substituting the values:
h = √(180.2^2 - (230.5/2)^2)
h = √(32544.04 - 26519.0125)
h = √(6037.0275)
h ≈ 77.7
Therefore, the height of the pyramid is approximately 77.7 meters, rounded to the nearest tenth.
that's wrong
Apologies for the mistake. Let's calculate the correct height of the pyramid.
Using the Pythagorean theorem, we have a right triangle with the slant height (l) as the hypotenuse, the height (h) as one of the legs, and half the length of the base edge (b/2) as the other leg.
We are given that the base edge (b) is 230.5 m and the slant height (l) is 180.2 m.
Using the Pythagorean theorem formula:
l^2 = h^2 + (b/2)^2
Substituting the values:
(180.2)^2 = h^2 + (230.5/2)^2
32544.04 = h^2 + 13202.625
h^2 = 32544.04 - 13202.625
h^2 = 19341.415
h ≈ √19341.415
h ≈ 139.2
Therefore, the height of the pyramid is approximately 139.2 meters, rounded to the nearest tenth.
Using the Pythagorean theorem, we have a right triangle with the slant height (l) as the hypotenuse, the height (h) as one of the legs, and half the length of the base edge (b/2) as the other leg.
We are given that the base edge (b) is 230.5 m and the slant height (l) is 180.2 m.
Using the Pythagorean theorem formula:
l^2 = h^2 + (b/2)^2
Substituting the values:
(180.2)^2 = h^2 + (230.5/2)^2
32544.04 = h^2 + 13202.625
h^2 = 32544.04 - 13202.625
h^2 = 19341.415
h ≈ √19341.415
h ≈ 139.2
Therefore, the height of the pyramid is approximately 139.2 meters, rounded to the nearest tenth.
its wrong
Apologies for the confusion. Let's recalculate the height of the pyramid correctly.
Using the Pythagorean theorem, we can find the height of the pyramid (h) as follows:
l^2 = h^2 + (b/2)^2
where l is the slant height and b is the base edge.
Given that the base edge (b) is 230.5 m and the slant height (l) is 180.2 m, we can substitute these values into the formula:
(180.2)^2 = h^2 + (230.5/2)^2
32544.04 = h^2 + 13202.5^2
32544.04 = h^2 + 17448.2025
Subtracting 17448.2025 from both sides:
15095.8375 = h^2
Taking the square root of both sides:
h ≈ √15095.8375
h ≈ 122.9
Therefore, the height of the pyramid is approximately 122.9 meters, rounded to the nearest tenth.
Using the Pythagorean theorem, we can find the height of the pyramid (h) as follows:
l^2 = h^2 + (b/2)^2
where l is the slant height and b is the base edge.
Given that the base edge (b) is 230.5 m and the slant height (l) is 180.2 m, we can substitute these values into the formula:
(180.2)^2 = h^2 + (230.5/2)^2
32544.04 = h^2 + 13202.5^2
32544.04 = h^2 + 17448.2025
Subtracting 17448.2025 from both sides:
15095.8375 = h^2
Taking the square root of both sides:
h ≈ √15095.8375
h ≈ 122.9
Therefore, the height of the pyramid is approximately 122.9 meters, rounded to the nearest tenth.
1 answer