The mosaic of the Polygonal Pools at the Math World aquarium is
almost complete. Different
shaped pools hold different colored fish. The pools fit together
like a puzzle.
There is one space left in which the final pool will be installed.
Two lengths of expensive copper
sheathing that form the sides of the pool have already been cut.
They are 6 meters and 7
meters long. The last pool must also fit into a 40° angle.
You are an engineering consultant who has been summoned to help
Math World choose the
best possible design for the final pool. Your job is to find all
possible triangles that could be built,
and make a recommendation for which one is the best.
You will submit your findings to the Design Board (aka Mrs.
Fontaine), and the last pool will be
constructed based on your recommendation.
Your report must include the following components:
1. There are 3 unique triangles that can be formed using a 40°
angle, a 6 meter side, and
a 7 meter side. Draw each of the possible configurations. (Remember
that rotations and
reflections don’t count as different triangles!)
2. How many total triangles are possible based on the 3
configurations? (Remember that it
helps to have your diagrams for SSA problems drawn in the same way
as we drew them
in the notes when assessing The Ambiguous Case...)
3. Solve all possible triangles identified in parts (1-2)
4. Draw and label diagrams of all triangles
5. Find the area of all triangles using Heron’s Formula
6. State your recommendation for which of the possible triangles is
the best choice for Math
World. (Explain your reasoning in complete sentences and support
your choice with facts
from your work.)