Question

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.

Answer 1

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.

`\begin{gathered} 13+14\ge16 \\ 27\ge16 \\ \\ 14+16\ge13 \\ 30\ge13 \\ \\ 13+16\ge14 \\ 29\ge14 \end{gathered}`

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:

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

Obtuse:

`c^2>a^2+b^2`

For the given triangle;

- Find the square of the longest side:

`16^2=256`

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

`13^2+14^2=169+196=365`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