Question

given the following side lengths of a triangle, use the pythagorean theorem to determine whether the triangle is a right triangle.
$a = 39$ in
$b = 89$ in
$c = 99$ in
show your work here

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\) (where \(c\) is the hypotenuse, the longest side). Here, \(c = 99\) in, \(a = 39\) in, \(b = 89\) in. First, calculate \(a^2 + b^2\).
\(a^2 = 39^2 = 1521\), \(b^2 = 89^2 = 7921\), so \(a^2 + b^2 = 1521 + 7921 = 9442\).

Step2: Calculate \(c^2\)

\(c^2 = 99^2 = 9801\).

Step3: Compare \(a^2 + b^2\) and \(c^2\)

Since \(9442
eq 9801\), \(a^2 + b^2
eq c^2\).

Answer:

The triangle with side lengths \(a = 39\) in, \(b = 89\) in, and \(c = 99\) in is not a right triangle.