• Classify triangles based on their angles and side lengths
• Determine the measure of the third angle in a triangle when the measures of two angles are given
• Apply properties of similar triangles to find unknown side lengths
• Use the Pythagorean theorem to calculate unknown side lengths in triangles

Triangle Troupe: A Physics Adventure at the Circus

You have been recruited to help Luca and Mia, two physics students who are working as interns at a popular circus during the summer break. They have been asked to use their knowledge of triangles to help with various tasks around the circus. Ready to help?

 

Luca and Mia are setting up a large circus tent which has a triangle at its front. The triangle has angles [latex]45°[/latex], [latex]45°[/latex], and [latex]90°[/latex].

Now that the circus tent is set up the clowns can preform. Luca is helping the clowns get ready for their show. He notices the clown’s hat is made of fabric that forms a triangle with sides of equal length. If all three sides of the triangle are each [latex]7[/latex]cm, which type of triangle does the hat represent?

While Luca is helping the clowns get ready, Mia is checking on the lights for the show. Mia decides new spotlight pattern is needed. Her new pattern forms a triangle with angles [latex]47°[/latex], [latex]102°[/latex], and [latex]31°[/latex]. What type of triangle is she using for her design?