The sides of a triangle are 61,39, and 97. Use the Pythagorean Theorem to determine if the triangle is right,acute, or obtuse. Answer Attemptiout of 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 hypotenuse and \(a\) and \(b\) are the other two sides.<br /><br />## Step 2<br />In this problem, the sides of the triangle are 61, 39, and 97. The largest side is 97, so we will consider this as the hypotenuse.<br /><br />## Step 3<br />We need to compare the square of the hypotenuse with the sum of the. If the square of the hypotenuse is greater than the sum of the squares of the other two sides, the triangle is obtuse. If the square of the hypotenuse is equal to the sum of the squares of the other two sides, the triangle is right. If the square of the hypotenuse 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:<br />### \(a^2 = 61^2 = 3721\)<br />### \(b^2 = 39^2 = 1521\)<br />### \(c^2 = 97^2 = 9409\)<br /><br />## Step 5<br />Now, we compare \(c^2\) with \(a^2 + b^2\):<br />### \(a^2 + b^2 = 3721 + 1521 =)<br />### \(c^2 = 9409\)<br /><br />## Step 6<br />Since \(c^2 > a^2 + b^2\), the triangle is obtuse.