Question

Determine if the following sides would form an acute, obtuse or right triangle16 feet, 11 feet, 4 feetAcute TriangleRight TriangleObtuse TriangleNot a Triangle

Answer 1

Step 1:

To determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute.

However, if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse.

Step 2:

`\begin{gathered} 11^2\text{ + 4}^2\text{ } \\ 121\text{ + 16} \\ =\text{ 137} \\ 16^2\text{ = 256} \end{gathered}`

Step 3

`\begin{gathered} 11^2\text{ + 4}^2\text{ < 16}^2 \\ 137\text{ < 256} \end{gathered}`

Final answer

Consequently, the triangle is obtuse.