The purpose of this discussion is to review students’ strategies for finding unknown side lengths of right triangles.

After students have completed their work, share the correct answers and ask students to discuss the process of solving the problems. Here are some questions for discussion:

• “What information did you need to ask for?” (what letters and where they go, an acute angle and a side length)
• “What could you figure out once you knew angle  was the right angle?” (The legs of the right triangle both have the letter , and the hypotenuse uses the other two letters.)

Highlight for students that drawing a diagram and labeling it with the information provided is an important strategy. It’s too easy to forget something or mix up information without a clear diagram to work from.

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Invite 2–3 students to share the norm they chose and how it supported the work of the group or a realization they had about a norm that would have worked better in this situation. Provide these sentence frames to help students organize their thoughts in a clear, precise way:

• “I picked the norm ‘.’ It really helped me/my group because .”
• “I picked the norm ‘.’ During the activity, I realized the norm ‘’ would be a better focus because .”

If students struggle with the city hall question, prompt them to draw a diagram with the information they know.

The purpose of this discussion is to reason about differences between exact answers and calculated answers.

Display this image of the Philadelphia City Hall:

“The exact heights are 829.8 meters for the Burj Khalifa and 548 feet for City Hall. Why don’t those numbers match your calculations?” (Rounding or measurement error. An angle that's slightly off can make a big difference when we work with large numbers.) “Is it reasonable to assume you are accurate to the nearest tenth in this case?” (No, the provided measurements were rounded to the nearest ten meters or hundred feet, so our usual rounding scheme doesn't apply.)