The sides of a triangle are 96,83 and 66. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse. Answer Attempt sout of 2 The triangle is square because the square of the largest side square the sum of the squares of the other two sides.

## Step 1<br />The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.<br /><br />## Step 2<br />In this problem, the sides of the triangle are 96, 83, and 66. The largest side is 96, so we will consider this as the hypotenuse.<br /><br />## Step 3<br />We need to compare the square of the largest side with the sum of the squares of the other two sides. If the square of the largest side is equal to the sum of the squares of the other two sides, the triangle is right-angled. If the square of the largest side is greater than the sum of the squares of the other two sides, the triangle is obtuse. If the square of the largest side is less than the sum of the squares of the other two sides, the triangle is acute.<br /><br />## Step 4<br />Let's calculate the squares of the sides:<br />### \(a^2 = 66^2 = 4356\)<br />### \(b^2 = 83^2 = 6889\)<br />### \(c^2 = 96^2 = 9216\)<br /><br />## Step 5<br />Now, let's compare \(c^2\) with \(a^2 + b^2\):<br />### \(c^2 = 9216\)<br />### \(a^2 + b^2 = 4356 + 6889 = 11245\)<br /><br />## Step 6<br />Since \(c^2\) is less than \(a^2 + b^2\), the triangle is acute.