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Geometry Lesson
Teacher’s name: ___Cara Pruiett_________________
Subject: Geometry
Date: __November 18, 2008 ___
Grade Level: __9-12 _Topic: _Trigonometric Functions_
Essential Questions/Big Ideas:
 How can trigonometric functions be used to determine lengths of sides and angle measures of
a right triangle?
Learning Objectives:
VA SOL: Standard G.7 The student will solve practical problems involving right triangles by
using the Pythagorean Theorem, properties of special right triangles, and right triangle
trigonometry. Solutions will be expressed in radical form or as decimal approximations.
NCTM: In grades 9-12 all students should Use trigonometric relationships to determine lengths and angle measures.
Students will understand:
 The relationship between the sides and angles of a right triangle can be represented using
trigonometric functions.
 The relationship between the sides and angles of a right triangle can be useful in many
real-world situations.
Students will know:
 Trigonometric functions: Sine, Cosine, Tangent
 How to use these functions on a graphing calculator
 Acronym to remember trigonometric functions: SOH CAH TOA
Students will be able to:
 Given a side and an angle of a right triangle, use trigonometric functions to find the
remaining sides and angle
 Given two sides of a right triangle, use trigonometric functions to find the remaining side
and angles
Student and Teacher Activities with Estimated Time Blocks:
1. Hook: Draw a right triangle on the board
with only one given side and one given angle.
Ask the students to determine if and how they
can find the two unknown sides and the
unknown angle. Write their answers on the
board, and discuss each answer as a class to
determine why they will or will not work. (At
this point the students have only used the
1. The students will discuss with the students
around them how they think they could find
the unknown sides and unknown angles of a
right triangle drawn on the board. They will
give their answers to the teacher to be written
on the board and then discussed as a class.
Answer the questions asked by the teacher
when called upon.
Pythagorean Theorem to find missing sides of
triangles. They should realize that they will
have difficulty finding a missing side when
they are only given one side of the triangle.
They will also realize that they can only find
missing angles when given two of the angles in
a triangle.) Ask the students if they will need to
find another method to find unknown sides and
angles in these special cases. (15 minutes)
What are the different methods we have so
far that can help us find unknown sides and
angles of a right triangle? (Knowledge) Do
we need another way to find unknown sides
and angles of right triangles? (Evaluate)
2. Introduce students to sine, cosine, and
tangent using a right triangle. Explain the
abbreviations for these trigonometric functions
(sin, cos, and tan), how they are pronounced
(not pronounced literally, still use the actual
terms sine, cosine, and tangent when reading
them), how they can be used (only on right
triangles!!), and how to find their functions on
a graphing calculator. Ask the students to recall
what the parts of a right triangle are called
according to a given angle (opposite side,
adjacent side, and hypotenuse). (10 minutes)
What are the different parts of a right
triangle called? (Knowledge)
3. Show students the acronym SOH CAH
TOA, what each letter stands for (sine,
opposite, hypotenuse, cosine, adjacent,
hypotenuse, tangent, opposite, adjacent), and
what it means (sin(x)=opp/hyp,
cos(x)=adj/hyp, tan(x)=opp/adj, where x is an
angle measure.) (Can also suggest the
acronym: Some Officers Have Curly Auburn
Hair Till Old Age and let them decide which
one is easier for them to remember.) Do an
example problem on the board of how to use
each of the three trigonometric functions on a
right triangle. Show the students how to
perform the appropriate calculations on a
graphing calculator to complete the problem.
In review, ask the students to explain what
2. The students will take notes on their own
paper and ask questions if they need
clarification. They will practice finding the
trigonometric functions on their own graphing
calculators. Answer the questions the teacher
asks when called upon.
3. The students will take notes on their own
paper and ask questions if they need
clarification. They will follow along on the
example problems as the teacher shows them
the solutions. They will also practice using
their graphing calculators to find the solutions.
The students will answer the questions asked
of them by the teacher.
unknown values can be found using these
trigonometric functions (angles, hypotenuse,
adjacent, and opposite sides.) Ask the students
how they could use these functions to solve
real-world problems in professions other than
mathematics (architecture, landscaping,
engineering, etc.) (10 minutes)
What unknown values can be found using
these trigonometric functions? (Analysis)
How might these functions be used to solve
real-world problems in other professions?
(Evaluate)
4. Ask students to discuss how the
trigonometric functions explain the
relationship between sides and angles of a right
triangle (the functions express the sides of a
triangle as ratios as compared to the angles.)
Write their answers on the board. Check for
student understanding before moving on; go
over the main ideas again if necessary or show
them another example problem. Give students
a worksheet of multiple problems involving
various trigonometric functions and have them
work in pairs to complete the worksheet. Post
an answer key at the front of the room for
students to use to check their answers when
they are done. Walk around the room and
answer any questions that students may have.
(45 minutes)
How do the trigonometric functions explain
the relationship between sides and angles in
right triangles? (Synthesis)
5. Closure: When the students finish their
worksheets, collect them and grade them. Give
students the following exit slip before the end
of class. (10 minutes)
Exit Slip (Formative assessment): What are
the three trigonometric functions? What is the
acronym we use to remember how to use
them? Given a triangle with one angle measure
of 30 degrees, one of 90 degrees, and a
hypotenuse of length 7, find the lengths of the
two missing sides and the missing angle.
4. The students will discuss trigonometric
functions and how they explain the relationship
between sides and angles in right triangles.
They will tell the teacher their answers to be
written on the board. The students will let the
teacher know if they are unclear on anything
they have learned so far in the lesson. The
students will then complete a worksheet with a
partner and check their answers with the
answer sheet posted at the front of the room
when they are done.
5. The students will turn in their worksheets
and then complete an exit slip before the end of
class.
Materials Needed for the Lesson:
 Worksheet
 Graphing Calculators
Resources:
 http://www.sosmath.com/trig/Trig2/trig2/trig2.html
 http://www.intmath.com/Trigonometric-functions/Trig-functions-intro.php