Question

a triangle has sides with lengths of 39 yards, 86 yards, and 89 yards. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 39\), \(b = 80\), and \(c = 89\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=39^{2}+80^{2}=1521 + 6400=7921\)

Step3: Calculate \(c^{2}\)

\(c^{2}=89^{2}=7921\)

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.

Answer:

yes