Lesson: 5-1
Concept/Topic: The Pythagorean Theorem
General Outcome(s): Develop algebraic reasoning.
Specific Outcome(s): Algebra 1: Solve problems that require the manipulation and application
of formulas related to the Pythagorean theorem and the primary trigonometric ratios.
Required Materials: Access to smart board, unit foldable, scissors.
Corresponding Text: Lesson 7.1 The Pythagorean Theorem Pages 270–282
Procedures
1. Handout scissors and supplies to have students construct the unit foldable. Introduce the unit
of trigonometry for right angles.
2. Using the smart board have students complete the definition of hypotenuse in their unit
foldable. Tell them to label the hypotenuse in the diagram.
3. Have students copy the notes for Pythagoras’ Theorem into their unit foldable using your
smart board fill in the blank version.
4. Using the smart board notes have students complete solutions in their unit foldable to
solving triangles using Pythagoras’ Theorem.
Possible Solution Ex #1
a 2  b2  c2
15.2    26.3
2
2
 c2
Possible Solution Ex #2
a 2  b2  c2
a 2   32    39 
2
2
922.73  c 2
a 2   39    32 
30.4cm  c
a 2  497
2
a  22.3"
5. Assign: Drill & Practice I: Pythagoras’ Theorem.
6. Assign: Math Works 10 Build Your Skills Page 278 #1–8, 11 & 12.
2
Lesson: 5-2
Concept/Topic: The Sine Ratio
General Outcome(s): Develop algebraic reasoning.
Specific Outcome(s): Algebra 1: Solve problems that require the manipulation and application
of formulas related to the Pythagorean theorem and the primary trigonometric ratios.
Required Materials: Access to smart board, unit foldable.
Corresponding Text: Lesson 7.2 The Sine Ratio Pages 283–292
Procedures
1. Using the smart board have students complete the definition of opposite in their unit
foldable. Tell them to label the opposite side in the diagram.
2. Have students copy the notes for Sine Ratio into their unit foldable using your smart board
fill in the blank version.
3. Using the smart board notes have students complete solutions in their unit foldable to
solving triangles using the Sine Ratio.
Possible Solution Ex #1
opp
Sin  
hyp
x
Sin 34 
30.5
30.5  Sin 34   x
Possible Solution Ex #2
opp
Sin  
hyp
42
Sin 40 
x
x  Sin 40   42
17.1 cm  x
x
42
Sin 40
x  65 ft
4. Assign: Drill & Practice II: Sine Ratio.
5. Assign: Math Works 10 Build Your Skills Page 289 #1–8.
Lesson: 5-3
Concept/Topic: The Cosine Ratio
General Outcome(s): Develop algebraic reasoning.
Specific Outcome(s): Algebra 1: Solve problems that require the manipulation and application
of formulas related to the Pythagorean theorem and the primary trigonometric ratios.
Required Materials: Access to smart board, unit foldable.
Corresponding Text: Lesson 7.3 The Cosine Ratio Pages 293–300
Procedures
1. Using the smart board have students complete the definition of adjacent in their unit
foldable. Tell them to label the adjacent side in the diagram.
2. Have students copy the notes for Cosine Ratio into their unit foldable using your smart board
fill in the blank version.
3. Using the smart board notes have students complete solutions in their unit foldable to
solving triangles using the cosine Ratio.
Possible Solution Ex #1
adj
Cos  
hyp
x
Cos 38 
215
215  Cos 38   x
169 cm  x
Possible Solution Ex #2
adj
hyp
12.5
Cos 32 
x
x  Cos 32   12.5
Cos  
x
12.5
Cos 32
x  14.8"
4. Assign: Drill & Practice III: Cosine Ratio.
5. Assign: Math Works 10 Build Your Skills Page 297 #1–6, 8.
Lesson: 5-4
Concept/Topic: The Tangent Ratio
General Outcome(s): Develop algebraic reasoning.
Specific Outcome(s): Algebra 1: Solve problems that require the manipulation and application
of formulas related to the Pythagorean theorem and the primary trigonometric ratios.
Required Materials: Access to smart board, unit foldable, tape measures, Handout: Measuring
Unreachable Heights
Corresponding Text: Lesson 7.4 The Tangent Ratio Pages 301–306
Procedures
1. Using the smart board have students complete the remaining definitions in their unit
foldable. Tell them to draw the angles of elevation to and the angle of depression from the
top of the Eiffel tower to complete the diagrams.
2. Have students copy the notes for Tangent Ratio into their unit foldable using your smart
board fill in the blank version.
3. Using the smart board notes have students complete solutions in their unit foldable to
solving triangles using the Tangent Ratio.
Possible Solution Ex #1
opp
adj
x
Tan 54 
12.1
12.1Tan 54   x
Tan  
16.7 yd  x
Possible Solution Ex #2
opp
Tan  
adj
x
Tan 33 
15.75
15.75 Tan 33   x
10.23 km  x
4. Handout the attached activity Measuring Unreachable Heights. Divide your students into
groups of three and have them work through the activity. Point out the marks rubric to them
on the back so they know how they will be evaluated.
5. Assign: Drill & Practice IV: Tangent Ratio.
6. Assign: Math Works 10 Build Your Skills Page 305 #1–5, 7.
Measuring Unreachable Heights
1.
2.
3.
4.
5.
6.
Name(s): ___________________________
Arrange a group of three members and collect the needed supplies:
A copy of this handout
A scientific or graphing calculator
A tape measure
An inclinometer
Choose four high objects in your school to measure the height of. Estimate the height of
each object without measuring.
Using the inclinometer, measure the angle of elevation to each.
Without moving the inclinometer, use the tape measure to find the distance from the point of
the inclinometer to the base of the object (horizontally) and record in the table.
Use the tape measure at the same time to measure the height of the inclinometer off the
ground (vertically) and record in the table.
Repeat steps 2–4 for each of your objects.
Complete the table by using the correct trig ratio to calculate the height of each object. Show
your calculations and a diagram on the back side of this page.
Hint: You will need to add the height of the inclinometer off the floor to your overall height calculation.
Object
Estimated
Height
Angle of
Elevation
Distance
From
Inclinometer
to the Base
Distance
from
Inclinometer
to Floor
Calculated
Height
Calculations & Diagram for Object 1
Calculations & Diagram for Object 2
Calculations & Diagram for Object 3
Calculations & Diagram for Object 4
Mark Criteria
□ □ □ □ Estimates are reasonable.
□ □ □ □ Diagrams are correctly drawn and measurements are correctly labelled.
□ □ □ □ □ □ □ □ Calculations are correctly completed
□ □ Neatness
□ □ □ Cooperation
Mark Out of
4
4
8
1
3
20
Lesson: 5-5
Concept/Topic: Solving for Angles in Right Triangles
General Outcome(s): Develop algebraic reasoning.
Specific Outcome(s): Algebra 1: Solve problems that require the manipulation and application
of formulas related to the Pythagorean theorem and the primary trigonometric ratios.
Required Materials: Access to smart board, unit foldable.
Corresponding Text: Lesson 7.5 Finding Angles And Solving Right Triangles Pages 307–319
Procedures
1. Using the smart board have students complete the definition of adjacent in their unit
foldable. Tell them to label the adjacent side in the diagram.
2. Have students copy the notes for Solving for Angles into their unit foldable using your smart
board fill in the blank version.
3. Using the smart board notes have students complete solutions in their unit foldable to
solving triangles using the cosine Ratio.
Possible Solution Ex #1
Possible Solution Ex #2
Possible Solution Ex #3
opp 
 Sin
hyp 
opp 
 Sin
hyp 
adj 
 Cos
hyp 
Sin  
opp
hyp
Sin  
22
32
 22 

 32 
Sin  
opp
hyp
Sin  
11.3
15.4
8.5
 b  11.2 
7.6
9.2
 11.3 

 15.4 
 7.6 

 9.2 
  Cos 1 
  43
  47
  34
adj 
 Cos
hyp 
2
b 2  11.2    8.5 
2
Cos  
  Sin 1 
a 2  b2  c 2
2
adj
hyp
  Sin 1 
Possible Solution Ex #4
2
Cos  
2
b 2  53.19
Possible Solution Ex #5
Cos  
adj
hyp
Cos  
8.5
11.2
 8.5 
  Cos 

 11.2 
  41
opp 
 Tan
adj 
h
1
b  7.3'
65
7.5 ft
Tan  
opp
adj
h
7.5
7.5 Tan 65   h
Tan 65 
16.1 ft  h
180  90  41  49
4. Assign: Drill & Practice V: Choosing the Right Ratio & Drill & Practice VI: Solving Right
Triangles.
5. Assign: Math Works 10 Build Your Skills Page 311 #1–8.
6. Assign: Math Works 10 Practice Your New Skills Page 316 #1–9, 12.