Question

Determine if the triangle with the given sides is acute, obtuse, or right.80, 84, 116

Answer 1

Given: The sides of a triangle below

`\begin{gathered} side1=80 \\ side2=84 \\ side3=116 \end{gathered}`

To Determine: If the triangle is acute, obtuse or right

Solution

If it is right triangle, then the Pythagoras theorem would hold

`\begin{gathered} Pythagoras-Theorem \\ Hypothenuse^2=Opposite^2+Adjacent^2| \\ Hypothenuse=Longest-side \end{gathered}`

Therefore:

`\begin{gathered} 116^2=80^2+84^2 \\ 13456=6400+7056 \\ 13456=13456 \end{gathered}`

From the above calculation, we can conclude that the triangle is

RIGHT TRIANGLE