Respuesta :

Supernova

Answer:

Acute

Step-by-step explanation:

The Converse of the Pythagorean Theorem states that:

  • If [tex]a^2+b^2 > c^2[/tex] then the triangle is acute.
  • If [tex]a^2+b^2 < c^2[/tex] then the triangle is obtuse.
  • If [tex]a^2+b^2 = c^2[/tex] then the triangle is right.

The side lengths 8, 14, and 15 are given. We can assume the hypotenuse (or c) is the longest side length, so it is 15.

  • c = 15

It doesn't matter which order of the numbers are plugged in for a and b, so a and b will be 8 and 14.

  • a = 8
  • b = 14

Now we have to add [tex]a^2[/tex] and [tex]b^2[/tex] to see if the sum is greater than, less than, or equal to 15 (c).

  • [tex]a^2 + b^2[/tex]
  • [tex]8^2 + 14^2[/tex]

Calculate the rest of the problem.

  • [tex]8^2=64 \newline 14^2=196[/tex]
  • [tex]64+196=260[/tex]

We have to find what [tex]15^2[/tex] is before we can make a decision using the Converse of the Pythagorean Theorem.

  • [tex]15^2=225[/tex]

260 ([tex]a^2+b^2[/tex]) is greater than 225 ([tex]c^2[/tex]). This means that the triangle is acute because [tex]a^2+b^2>c^2[/tex].

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