missmargofargo
missmargofargo missmargofargo
  • 23-10-2019
  • Mathematics
contestada

Determine if the values 3, 5, and 7 represent the side lengths of a right triangle, an obtuse triangle, or an acute triangle. Justify your answer.

Respuesta :

maguimalz
maguimalz maguimalz
  • 24-10-2019

Answer:

It's an acute triangle.

Step-by-step explanation:

In a triangle ABC with longest side C:

If [tex]c^2>a^2+b^2[/tex] then ABC is acute

If [tex]c^2=a^2+b^2[/tex] then ABC is right

If If [tex]c^2<a^2+b^2[/tex] then ABC is obtuse

In this case A=3, B=5 and C=7. Let's see:

[tex]7^2 ? 3^2+5^2[/tex]

[tex]49 ?  9+25[/tex]

[tex]49 >  34 [/tex]

As 49 is bigger than 34, then ABC is acute.

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