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Mathematics, 06.05.2020 01:14 tingzontumbler8412

Audio Transcript: "I'm Jerome, and I'm really into snow sports — especially skiing and snowboarding. In fact, I just got a job at the local ski resort as an assistant to the manager. I'm realizing that there's a lot more to worry about than whether or not the ski lifts are running. [A picture is shown of Jerome; a young man with light-brown hair. A picture is shown of the snow-covered mountains.]

For example, I need to help manage the flow of downhill skiers, cross-country skiers, and snowboarders to minimize accidents. [A picture is shown of a skier who has fallen into the snow.]

My manager has asked me to work with Kayla, over in the safety office, to spot places where we might need extra fences or other safety equipment. [A picture is shown of a ski trail down the mountain.]

One location that poses a higher risk than others is where a slow beginner's run crosses a faster, more advanced black diamond run. [A picture is shown of children skiing down a gentle slope. A second picture is shown of a man snowboarding quickly down a steep slope.]

We're proposing the installation of fences to guide the ski traffic where one run intersects the other. They'd have to be angular. [A picture is shown of a fence along the side of a ski trail.]

I drew this diagram of the two ski slopes to help picture what is going on. [A diagram is shown of a wide blue arrow pointing downwards. A narrow purple arrow points to the lower right and intersects the blue arrow.]

There is already a partial fence at the corner right here. [An orange line is drawn along the corner created when the purple arrow first intersects the blue arrow.]

So we'll build that out and then install another here. We just need to know what these angles are. [A second orange line is drawn on the opposite side of the blue arrow between the blue arrow and the purple arrow.]

At this intersection, the edges for the downhill run are parallel, and the borders of the slow run are also parallel. [The sides of the blue arrow are outlined and marked as parallel. The sides of the purple arrow are outlined and marked as parallel.]

Kayla found a sketch showing that the existing fence has an angle of 35 degrees. [The angle created by the first orange line is marked as 35 degrees.]

We still need to figure out the angle of the new fence. I think we can use those parallel lines to figure out the second angle, but Kayla thinks we need to go out there and measure it.

What do you think? Who do you think is right?"

Question: What conjecture is being made? What key details are given? What is your plan of action?

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