A triangle has side lengths of 8cm, 15cm, and 17cm.classify it as acute, obtuse, or right
8^2 + 15^2 = 17^2
so, a right triangle
You would do well to recognize a few basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples
Well, it seems like this triangle needs a little humor injected into it! So here's a triangle joke for you:
Why was the math book sad?
Because it had too many problems!
Now, as for your triangle, let's figure out its classification. Since it has side lengths of 8cm, 15cm, and 17cm, we can use the Pythagorean theorem to see if it's a right triangle.
If the square of the longest side (17cm) equals the sum of the squares of the other two sides (8cm and 15cm), then it's a right triangle.
17^2 = 8^2 + 15^2
289 = 64 + 225
289 = 289
So, it's a right triangle! Ta-da! But remember, math jokes always work better than triangle classifications.
To classify the triangle as acute, obtuse, or right, we need to determine the relationship between the square of the longest side and the sum of the squares of the other two sides.
Let's define the side lengths as follows:
a = 8cm
b = 15cm (longest side)
c = 17cm
We can use the Pythagorean theorem to check if the triangle is right-angled.
According to the Pythagorean theorem, for a right-angled triangle, the square of the longest side (c) is equal to the sum of the squares of the other two sides (a and b).
Let's calculate the squares of the side lengths:
a^2 = 8^2 = 64
b^2 = 15^2 = 225
c^2 = 17^2 = 289
Now, let's check the relationship:
c^2 = a^2 + b^2
289 = 64 + 225
Since the equation holds true (289 = 289), we can conclude that the triangle is a right-angled triangle.
Therefore, the triangle with side lengths 8cm, 15cm, and 17cm is a right-angled triangle.
To classify a triangle as acute, obtuse, or right, we need to examine the relationship between the lengths of its sides.
In a right triangle, one of the angles is exactly 90 degrees, and it satisfies the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To determine if the given triangle is right, we can check if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Let's calculate it:
Side lengths:
a = 8 cm
b = 15 cm
c = 17 cm
To categorize it as a right triangle, we need to check if c^2 = a^2 + b^2.
Substituting the values:
17^2 = 8^2 + 15^2
289 = 64 + 225
289 = 289
Since the equation holds true, we can conclude that the triangle with side lengths of 8 cm, 15 cm, and 17 cm is a right triangle.