Course: Math 10 Foundations and Pre-Calculus
Stage 1 – Desired Results
Outcome:10.4 Develop and apply the primary trigonometric ratios (sine, cosine,
tangent) to solve problems that involve right triangles
Indicators:
a) Develop, generalize, explain and apply relationships between the ratios of side length and
angle sizes in similar triangles.
b) Demonstrate how to identify the hypotenuse of a right triangle and the adjacent side and
opposite side to an acute angle in that right triangle.
c) Solve problems, with or without the use of technology, involving one or more right triangles
by applying primary trigonometric ratios and/or the Pythagorean Theorem.
d) Create and solve problems that involve indirect and direct linear measurements by sing the
primary trigonometric ratios, the Pythagorean Theorem, and measure instruments such as a
clinometer or metre stick.
Enduring Understandings:
Students will understand that…
Essential Questions:
Missing pieces of right triangles can be found
indirectly or without measuring devices.
What are the relationships between sides in similar
right triangles?
What strategies are available to solve for missing
pieces of a right triangle?
Students will know:
Students will do:



Relationships exist between side lengths of
similar right triangles
How to identify the hypotenuse, adjacent
side and opposite side in relation to an
acute angle.
Missing parts of right triangles can be
found using primary trig ratios or
Pythagorean Theorem.



Develop, generalize, explain and apply the
relationships between the side lengths of
similar right triangles
Identify the hypotenuse, adjacent side and
opposite side in relation to an acute angle
in a right triangle.
Apply primary trig ratios for Pythagorean
Theorem to find missing angles or sides.
Stage 2 – Assessment Evidence
Formative (Pre-assessment, Self, …) :
Pre-assessment:
Measuring Inaccessible Heights.
Hand out sheet with practice questions
utilizing Pythagorean Theorem in different
Ramp It Up! – Unit Project.
ways.
Hand out sheet on solving ratio equations.
Hand out sheet on similar triangles.
Summative
Performance Tasks:
Unit Exam
Work on textbook assignments checking
answers and discussing results in class.
Exit cards.
Self Assessment – checklist on Chapter
Review.
Stage 3 – Learning Plan
Learning Activities:
Lesson 1 Pre-Assessment Activity.
1. Brainstorm with the students about what they already know about a right triangle.
Terminology – right angles, acute angles, hypotenuse, legs, sum of angles, longest side opposite right
angle, shortest side opposite smallest angle.
Discuss the formula: Hypotenuse2 = leg2 + leg2
Guide students through examples using formula in to find different sides in a right triangle.
Assign Master 2.1c – Check your understanding.
2.
Review solving a proportion type equation b 
x
a
and b  , x  0
a
x
Methods - clearing denominators or cross multiplication
Provide examples of solving both types of equations
Assign Master 2.1b – Check your understanding
Lesson 2 – Similar Triangles and Tangent Ratio
GeoGebra software application “Similar Right Triangle”
Key questions on the two triangles.
1. What is remaining the same in the two triangles?
2. What is changing in the two triangles?
3. Are the two triangles congruent?
4. Are the two triangles similar?
5. Note the ratio of long leg to short leg in each triangle.
6. How do the ratios between the two triangles compare.
7. How do the ratios between the triangles compare when the triangle size changes.
8. What does the value of each ratio depend upon?
Discuss the naming of the sides in relation to its acute angles. (opp, adj, hyp)
Discuss the TANGENT ratio.
Provide examples to find the tangent ratio of an angle given two legs in right triangle.
Provide examples to find the measure of an angle using the tangent ratio.
Assign questions page 75 3-9
Exit card – page 72 check your understanding #1.
Lesson 3 – Tangent Ratio and finding missing angles.
Discuss Angle of Inclination and where it is used in everyday life.
Provide examples to find angle of inclination.
Assign questions page 76 10-21.
Lesson 4 – Tangent Ratio to find missing lengths.
Entrance card – page 74 check your understanding #4
Discuss proportion type equations and the similarity to a Tangent Ratio.
Brainstorm how the length of a missing leg could be found if the acute angle and other leg are known in the
right triangle.
Provide sample questions where finding missing leg lengths are required.
Assign questions page 82 #3-10, 15
Lesson 5 - Math Lab – Measuring inaccessible distances
Students create a clinometer and use it to measure inaccessible heights.
Determine – height of scoreclock in gym, height of flagpole, height of gymnasium from outside.
Submit math lab results along with assignment page 86 #2.
Lesson 6 – Sine and Cosine Ratios
GeoGebra software application “Similar Right Triangle”
Compare the two triangles and the ratio of short leg to the hypotenuse
Compare the two triangles and the ratio of the long leg to the hypotenuse.
Review labeling sides of a triangle in relation to an acute angle.
Introduce SOH CAH TOA.
Work through examples to find the sin and cos of an acute angle.
Provide examples to find the measure of an acute angle given any two of the three sides of a right triangle.
Discuss Angle of Elevation and Angle of Depression.
Assignment page 95 3-13, 17
Lesson 7 – Sine and Cosine Ratio to find missing lengths.
Discuss page 97 – construct Understanding. Why is this an inaccessible distance? Which trig ratio could
be used to find this distance?
Provide examples finding missing side lengths (including hypotenuse).
Assign page 101 3-9, 11
Lesson 8 – Application of the Trigonometric Ratios
Discuss Making Connections – page 105.
Introduce – Ramp It Up project. Page 128, 129.
Provide examples to solve all missing parts of a right triangle given two sides.
Provide examples to solve all missing parts of a right triangle given one side and one acute angle.
Assignment page 111, 3,4,6-11,15
Lesson 9 – Solving diagrams with more than one triangle
Start class with a short quiz (solving one triangle) – Entrance pass
Correct quiz as a class and return to students.
Provide examples solve problems where there are more than one right triangle.
Assignment page 118 3,4,6,8-15
Lesson 10 – Students work on Review Assignment page 124.
Provide students with Self Assessment and Review chart (page 47,48 Teacher Resource)
Lesson 11, 12
Ramp It Up – Project
Lesson 13
Unit test
Resources Needed
Pearson Textbook
Geogebra software (free download from internet)
“Similar Right Triangles” application for Geogebra (downloaded from Internet)
Trigonometry
Unit Test
Foundations & Pre Calculus 10
Name
For questions 1 and 2, choose the correct answer.
1. In DEF , how many of these statements are true?
12
13
5
tan D 
12
cos D 
a.
b.
c.
d.
sin D 
5
13
tan F  2.4
1 is true.
2 are true.
3 are true.
All are true.
2. In right DEF , with E  90 , which statement is false?
As D decreases:
a.
b.
c.
d.
sin D increases.
sin F increases.
cos D increases.
cos F increases.
3. Solve each of the following triangles. Give all answers to the nearest tenth.
a.
b. Right KMN with M  90, N  26 and KN  15.0cm .
c. When you solved the triangles in part a, b did you use the same strategies?
If you answer yes, describe your strategy.
If you answer no, explain why you used different strategies.
4. The angle of inclination of a conveyor is 8 . The conveyor rises 0.75 metres.
What is the length of the conveyor? Give your answer to the nearest hundredth of
a metre.
5. A helicopter is hovering at a height of 300m. From the helicopter, the angle of
depression to the top of a wind turbine is 40 and the angle of depression to the
base of the turbine is 48 . Determine the height of the wind turbine, to the nearest
tenth of a metre.