Question

Use the pythagorean Theorem to determine which sets of numbers is a Pythagorean Triple:
11, 60, 62


20, 21, 29


9, 12, 14

Answer 1

Revisit the sets of numbers in question 2. Which one would form a right triangle? Which one would form an acute triangle? Which one would form an obtuse triangle? Explain how you know.
this is the second part of the question

Answer 2

but which of the other set of numbers would be considered and obtuse triangle you only presented one set

Answer 3

Let's plug in the numbers into the Pythagorean Theorem (a^2 + b^2 = c^2) and see if it holds true:

1. For 11, 60, 62:
11^2 + 60^2 = 121 + 3600 = 3721
62^2 = 3844
3721 is not equal to 3844, so 11, 60, 62 is not a Pythagorean Triple.

2. For 20, 21, 29:
20^2 + 21^2 = 400 + 441 = 841
29^2 = 841
Since 841 = 841, 20, 21, 29 is a Pythagorean Triple.

3. For 9, 12, 14:
9^2 + 12^2 = 81 + 144 = 225
14^2 = 196
225 is not equal to 196, so 9, 12, 14 is not a Pythagorean Triple.

Therefore, the only Pythagorean Triple from the sets of numbers given is 20, 21, 29.

Answer 4

To determine whether the triangle formed by the set of numbers is a right, acute, or obtuse triangle, we must compare the sum of the squares of the two shorter sides with the square of the longest side.

In set 2 (20, 21, 29):
20^2 + 21^2 = 400 + 441 = 841
29^2 = 841

Since 841 = 841, this set forms a right triangle because the sum of the squares of the two shorter sides is equal to the square of the longest side.

Now, let's determine whether the triangle is acute or obtuse.

For a triangle to be acute, the sum of the squares of the two shorter sides should be greater than the square of the longest side.
For a triangle to be obtuse, the sum of the squares of the two shorter sides should be less than the square of the longest side.

In set 2 (20, 21, 29):
20^2 + 21^2 = 841
29^2 = 841

Since 841 = 841, the triangle is right. Thus, it cannot be acute or obtuse. This means that the triangle formed by the numbers 20, 21, and 29 is a right triangle.

Answer 5

Let's revisit the other set of numbers to determine whether the triangle formed would be acute, right, or obtuse.

For set 3 (9, 12, 14):
9^2 + 12^2 = 81 + 144 = 225
14^2 = 196

Since 225 is greater than 196, the sum of the squares of the two shorter sides is greater than the square of the longest side. This means that the triangle formed by 9, 12, and 14 would be an obtuse triangle. The obtuse triangle is formed when the square of the longest side is less than the sum of the squares of the two shorter sides.

Therefore, the set of numbers 9, 12, and 14 would form an obtuse triangle. Thank you for pointing out the need to revisit the other set of numbers.