Question

the sides of a triangle are 49, 76, and 84. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse. the triangle is right because the square of the largest side equals the sum of the squares of the other two sides.

Explanation:

Step1: Calculate the squares of the sides

Let \(a = 49\), \(b=76\), \(c = 84\) (where \(c\) is the largest side).
\(a^{2}=49^{2}=2401\), \(b^{2}=76^{2}=5776\), \(c^{2}=84^{2}=7056\)

Step2: Check the relationship between \(a^{2}+b^{2}\) and \(c^{2}\)

Calculate \(a^{2}+b^{2}\): \(2401 + 5776=8177\)
Since \(8177>7056\) (i.e. \(a^{2}+b^{2}>c^{2}\))

Answer:

The triangle is acute.