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If this represents the sides of a triangle, classify it by it being an acute triangle, obtuse triangle, right triangle, or not being a triangle.

If This Represents The Sides Of A Triangle Classify It By It Being An Acute Triangle Obtuse Triangle Right Triangle Or Not Being A Triangle class=

Sagot :

1. Determine if it is a rtiangle by using the triangle inequality: the sum of any two sides of a triangle is greater than or equal to the third side.

[tex]\begin{gathered} 13+14\ge16 \\ 27\ge16 \\ \\ 14+16\ge13 \\ 30\ge13 \\ \\ 13+16\ge14 \\ 29\ge14 \end{gathered}[/tex]

It is a triangle

2. To classify a triangle knowing its sides you use the next: In a triangle ABC with longest side c

Acute:

[tex]c^2Right:[tex]c^2=a^2+b^2[/tex]

Obtuse:

[tex]c^2>a^2+b^2[/tex]

For the given triangle;

- Find the square of the longest side:

[tex]16^2=256[/tex]

-Find the sum of the squares of the other sides:

[tex]13^2+14^2=169+196=365[/tex]As the sum of the squares of the to smallest sides (365) is greater than the square of the longest side (256) it is an acute triangle.Answer: Acute triangle
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