Question

ilya builds a slide that is 2.9 meters long. it is 1.5 meters above the ground. he wants to determine the distance from the bottom of the slide to the base of the ladder leading up to the slide. which diagram represents this situation?

Explanation:

Step1: Analyze the problem

We need to find the diagram that represents the situation where the slide is \(2.9\)m (hypotenuse), height is \(1.5\)m (one - leg of the right - triangle), and we want to find the distance from the bottom of the slide to the base of the ladder (the other leg of the right - triangle).

Step2: Check the right - triangle sides

In a right - triangle, the hypotenuse is the longest side. In a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), by the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), and \(c=\sqrt{a^{2}+b^{2}}\). Here, \(c = 2.9\)m (hypotenuse), and one leg \(a = 1.5\)m. The other leg \(b=\sqrt{2.9^{2}-1.5^{2}}\). Since the hypotenuse is the longest side in a right - triangle, the side labeled \(2.9\)m should be the hypotenuse (the side opposite the right - angle and the longest side of the right - triangle).

Answer:

The first diagram (where the side labeled \(2.9\)m is a leg and \(1.5\)m is the other leg is incorrect as \(2.9>1.5\) and the hypotenuse should be the longest side). The second diagram (where \(2.9\)m is a leg and \(1.5\)m is the hypotenuse is incorrect since \(2.9>1.5\)). The third diagram (where \(2.9\)m is the hypotenuse and \(1.5\)m is a leg is correct). The fourth diagram (where \(2.9\)m is a leg and \(1.5\)m is the other leg is incorrect as \(2.9>1.5\) and the hypotenuse should be the longest side). So the correct diagram is the third one.