Triangle Troupe: A Physics Adventure at the Circus Cont.

Luca has been asked to create scaled-up props for the clowns performance. He needs a small tortilla chip and giant one for one of the clowns bits. He’s starting with a triangular tortilla chip with side lengths of [latex]2.5[/latex] inches, [latex]2.2[/latex] inches, and [latex]3[/latex] inches. If the longest side of the scaled-up tortilla chip is [latex]72[/latex] inches, what are the lengths of its other two sides?

Once the clowns are finished performing it is time for the acrobats. An acrobat at the circus is planning a new act involving a triangular rigging point. To meet safety requirements, the triangle formed must be an acute triangle. Two of the angles of the triangle are [latex]42°[/latex].

As a fun break from their duties, Luca and Mia decide to set up a badminton net on the circus grounds. Each end of the net is attached to a pole which is stabilized with a wire that attaches at the top of the pole and stretches out to a stake in the ground. To decide where to set up the net, they need to calculate the distance from the foot of the pole to the stake. The pole is [latex]5[/latex] feet tall and the wire is [latex]8[/latex] feet long.

Great job today utilizing your understanding of angles, triangles, and their properties in various scenarios at the circus. The skills you’ve honed here, particularly the ability to visualize and calculate geometric properties, will be invaluable in many areas of study, including physics, engineering, and design. The fun and excitement of the circus is bringing math to life!