Question

determine if the figure shown is a right triangle.

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side (hypotenuse) and \(a\) and \(b\) are the other two sides.

Step2: Identify the sides

Let \(a = 16\), \(b = 28\), and \(c = 34\). Calculate \(a^{2}+b^{2}\) and \(c^{2}\).
\[a^{2}=16^{2}=256\]
\[b^{2}=28^{2}=784\]
\[a^{2}+b^{2}=256 + 784=1040\]
\[c^{2}=34^{2}=1156\]

Step3: Compare

Since \(a^{2}+b^{2}=1040
eq1156 = c^{2}\), the triangle does not satisfy the Pythagorean theorem.

Answer:

No, the figure is not a right - triangle.