Grade 10 Essential Math Unit 7: Trigonometry of Right Triangles
Learning Goal(s):
1) solve problems involving right triangles using the Pythagorean theorem
2) solve problems that require the manipulation and application of formulas related to:
a. the Pythagorean theorem
b. primary trigonometric ratios
Key Terms:
angle of depression
angle of elevation
leg
cosine
tangent
hypotenuse
Pythagorean theorem
sine
Learning Activities:
Complete the following questions, and make sure to check your answers at the back of the textbook.
There is an answer key there. Make sure to ask questions in class if you are not getting the right
answers.
____p. 278-282 #1-12 (or Section 7.1 in booklet)
____p.289-291 #1-10 (or Section 7.2 in booklet)
____p. 297-299 #1-9 (or Section 7.3 in booklet)
____p.305-306 #1-8 (or Section 7.4 in booklet)
____p. 311-314 #1-9 (or Section 7.5 in booklet)
____p.316-319 #1-13 (Review)
Assessment:
This unit will have two assessment pieces – a project and a test. The test will be based on the review.
You will hand in the project by the date of the test. The test and the project will each be worth 5% of
your final grade.
______________ Practice Test date (to be determined together)
______________ Unit Test date (to be determined together)
_____________ _ Unit Project due (to be determined together)
ESM Gr.10 Unit 7 Project: Design a Staircase for a Home
To do checklist:
______ Read p.271“Project Overview”
______ Read p.271 “Get Started” to begin brainstorming for your project. Write down your ideas.
(As in - answers the questions).
_____ Read p.271 “Final Presentation Checklist” to get an idea of what your final project should be.
_____ Read p.300 “Making a Scale Diagram or a Scale Model” and complete a scale drawing of your
designed staircase. Keep this to hand in later as part of your project.
_____ Read p. 315 “Compiling your work and preparing your presentation”.


Make sure that you have completed all of the 4 requirements listed under “Your
package includes: ”
Answer all 4 questions listed under “Be prepared to answer questions about your work,
including:”
You will hand in:
1) A scale drawing of your staircase – make sure that it meets the criteria set out on p.271 of being
9’11’’ high with a maximum floor area available of 11’ x 11’.
2) Accurate measurements of each part of the staircase on your scale diagram. Make sure that the
measurements make practical sense. You may wish to research what typical height and depth
of stairs tend to be. (E.g. stairs that are 2 feet high and 6 inches deep would be very annoying to
use)
3) Steps for the work involved are explained, including tools and instruments that will be needed
4) At least one pair of similar figures labeled in your diagram. Make sure to label congruent angles
are labeled appropriately (e.g. A and A’). Also, include calculations to prove that the
corresponding side ratios are all the same to prove the figures are similar.
5) The measurements listed on your diagram are calculated in imperial units (feet and inches)
6) A written “discussion” as to why you designed your staircase as you did, including the 4
questions that you are required to answer on p.315.
ESM Gr.10 Unit 7 Project Rubric: Design a Staircase for a Home
0
Not submitted
1
1 criteria met
2
2 criteria met
2) Scale
Drawing
measureme
nts
Not submitted
1 criteria met
2 criteria met
3) Written
steps
Not submitted
1 criteria met
2 criteria met
4) Similar
figures
Not submitted
1 criteria met
2 criteria met
5) Imperial
Units
labeled
Not submitted
6) Written
discussion
Not submitted
Few
measurements
are listed in
correct
imperial units
Few of the
questions are
answered
Most
measurements
are listed in
correct
imperial units
Most of the
questions are
answered
1) Scale
Drawing
3
All 3 criteria are met:
Fits 9’11’’ high
Fits 11’x11’ floor
area available
Scale included is
correct
All 3 criteria are met:
Accurate
Clearly labeled
Make sense
practically
All 3 criteria are met:
Clear
Numbered
Tools and
instruments
required included
One pair of similar figures
has:
Labeled
Congruent angles
labeled
appropriately (e.g.
A and A’)
Corresponding sides
ratios are calculated
and prove figures to
be similar
All measurements are listed
in correct imperial units
Discussion includes:
Answers to all four
questions listed on
p.315
Explanation as to
why you chose your
particular design
_____/18 = _____ %