II.ProblemSolvingActivity-TheCampingQuestion
- Students are going to use the geometric mean to figure out the altitude of a triangle.
- Here is the problem.
- “Mariah is going on a teen wilderness trip. She will be using a tent that is triangular in shape and she has been
told that the height of the tent can’t exceed nine feet. For this to be possible, the tent pole can not be greater
than nine feet. She has a diagram of her tent. Use what you have learned about the geometric mean and the
given the dimensions, to figure out the height of the tent. Will Mariah’s tent work for her trip or does she need
to get a different tent?” - Figure08.03.01
- Students first need to convert inches to feet. This will show them that the tent is divided into two 8 foot
sections. - Solution: 8× 8 = 64
√
64 = 8
- The height of the tent is 8 feet, so Mariah’s tent will fit the specifications of the trip.
III.MeetingObjectives
- Students will evaluate the geometric mean of various objects.
- Students will identify the length of an altitude using the geometric mean of a separated hypotenuse.
- Students will justify their answers.
IV.NotesonAssessment
- Check student work for accuracy.
- Did the students convert inches to feet correctly?
- Did they remember to multiply the dimensions of the divided hypotenuse?
- Did they come up with a solution of 8 feet for the altitude of the tent?
- Offer feedback/correction when needed.
Special Right Triangles
I.SectionObjectives
- Identify and use the ratios involved with right isosceles triangles.
- Identify and use the ratios involved with 30− 60 −90 triangles.
- Identify and use ratios involved with equilateral triangles.
- Employ right triangle ratios when solving real- world problems.
II.ProblemSolvingActivity-TriangleTiling
- For this activity, you will need to cut out a bunch of squares of different sizes. Each square needs to have a
diagonal dividing it into two right triangles. - Figure 08.04.01
- Each student is going to receive a square to work with.
- Tell students that they need to measure their square and figure out the length of the hypotenuse of each square.
- The measurements must be labeled on the back of the design.
- Then they can decorate the square however they would like.
- Finally, the students are going to create a square tiling on a piece of paper.
5.8. Right Triangle Trigonometry