Lesson Plan
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Angle of Elevation and Angle of Depression
Rationale
Student's need to formulate, and apply trigonometric ratios to solve real world problems.
Course
Geometry
Grade Levels
10th Grade
Related Academic Standards
Commonwealth of Pennsylvania Standards and Anchors
2.5.G.A Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the
plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate
contexts.
2.10.G.A Identify, create, and solve practical problems involving right triangles using the trigonometric ratios and the
Pythagorean Theorem.
G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles.
Big Ideas
Mathematical statements can be justified through deductive and inductive reasoning and proof.
Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures
in many equivalent forms.
Objects can be transformed in an infinite number of ways. Transformations can be described and analyzed
mathematically.
Patterns exhibit relationships that can be extended, described, and generalized.
Relations and functions are mathematical relationships that can be represented and analyzed using words, tables,
graphs, and equations.
Similarity relationships between objects are a form of proportional relationships. Congruence describes a special
similarity relationship between objects and is a form of equivalence.
Some geometric relationships can be described and explored as functional relationships.
Spatial reasoning and visualization are ways to orient thinking about the physical world.
There are some mathematical relationships that are always true and these relationships are used as the rules of
arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and
inequalities.
Concepts
2- and 3-dimensional figures
Analytic Geometry
Geometric Relations: Congruence and Similarity
Geometric Representations
Trigonometric Ratios
Competencies
Use concepts of congruence and similarity to relate and compare 2- and 3-dimensional figures, including
trigonometric ratios.
Use coordinates and algebraic techniques to interpret, represent, and verify geometric relationships.
Subjects/Courses
Geometry
Vocabulary
Angle of Elevation
Angle of Depression
Topography
Trigonometric ratios: sine, cosine, and tangent
geometric mean
proportions
Objectives
Students will create a diagram based on the given information in a word problem.
Students will differentiate among the trigonometric ratios and select the appropriate function.
Students will solve word problems using the appropriate function.
Essential Question(s)
What is the relationship between geometric concepts and algebraic procedures when solving
trigonometric functions?
How are right triangle relationships useful in solving real world problems?
Duration
84 minutes to 168 minutes 1 to 2 class periods
Materials
promethean board
handouts
TI 83 Graphing Calculators
textbooks
TI 83 Graphing Calculator program fr the promethean board
Suggested Instructional Strategies
Active Engagement , Modeling , Explicit Instruction , Inquiry Based
W : Students will incorporate their prior algabraic knowledge of solving a proportion and their new knowledge of
setting up a trigonometric function to find a missing angle.
H : Students will view various word problems involving angle of elevation and angle of depression and discuss how
to set up the correct trigonometric function to find the solution.
E : Students will summarize new information orally to show competency of the concepts acquired for themselves and
for their peers.
R : Students will work in groups or individually to discuss word problems, draw the appropriate diagrams, set up the
correct trig proportion and formulate a solution.
E : Teacher will observe the interaction and discussion between students to ensure that they have a good
understanding of the newly introduced mathematical concepts and can apply them to various situations to solve a
real world scenario.
T: Students can build on prior knowledge of algebraic problem solving techniques and current knowledge of
geometric and trigonometric principles to solve true to life word problems. Highly sequential thinkers may solve
problems entirely on their calculators while others may prefer to use a step by step approach. Intervention study
guides can be used to facilitate learning for those students who need remediation while enrichment sheets can be
used for those students who want to further increase the level of difficulty of the problems.
O: This lesson provides for a large group instruction, cooperative learning and peer evaluation. Students can show
creativity by creating their own word problems, exchanging them with a peer and finding the solut
Instructional Procedures
Teacher will present the questions " Where would you find an angle of elevation or depression? What geometric
shape is formed by these angles? How can we use trigonometry to find a solution?"
After a brief class discussion, the teacher will pass out flipchart notes and examples and use a flipchart presentation
to show how to solve for the missing angle or side. Students wil be called on to explain how to set up the problem
and then will solve it on the promethean board. Students will discuss how to best utilize the calculator to solve a trig
function. We will discuss and use the mnemonic device SOA-CAH-TOA to recall the trig functions :
sin= opposite leg
cos=adjacent leg
tan=opposite leg
hypotenuse
hypotenuse
adjacent leg
Students will then work in cooperative learning groups to set up and solve word problems involving trig ratios and
angle of elevation and depression. Student will then do those problems on the board and will orally explain how they
derived the solution.
Homework will be assigned.
Formative Assessment
Continuous formative assessment will be done through observation during small group instruction. Teacher will call
on students to go to the board ,solve their problem and explain how they derived the answer.
If remediation is needed, students cal go to glencoe.com, our on line study tool to solve additional problems in the
section.
Related Materials & Resources
Activinspire program and software
www.kuta software.com
www.glencoe.com
Author
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