Question

side ( m ) is approximately 6.1 units, side ( n ) is approximately 11.48 units, and side ( o ) is 13 units. what is the length of the hypotenuse of this triangle? how do you know?

Explanation:

Step1: Recall triangle angle - side relationship

In a right - triangle, the hypotenuse is the side opposite the right angle. Also, in a triangle, the larger side is opposite the larger angle. The sum of angles in a triangle is \(180^{\circ}\). Let's check the angles: \(28^{\circ}+62^{\circ}=90^{\circ}\), so the third angle is \(180-(28 + 62)=90^{\circ}\).

Step2: Identify the hypotenuse

In a right - triangle, the hypotenuse is the longest side. Given \(m = 6.1\), \(n=11.48\), \(o = 13\). Since \(6.1<11.48<13\).

Answer:

The length of the hypotenuse is \(13\) units. We know this because in a right - triangle (since \(28^{\circ}+62^{\circ}=90^{\circ}\)), the hypotenuse is the longest side, and among \(m = 6.1\), \(n = 11.48\), and \(o=13\), \(o = 13\) is the longest.