Lesson Plan: Applications of Trig Ratios
Lesson Objectives:
1. Use angles of depression and elevation to calculate horizontal, vertical and
diagonal distances.
2. Construct and use a quadrant and tape measure to measure angles of elevation and
calculate heights.
Materials: Calculators, Quadrant Construction Materials (see http://www.kyesworld.com/quadrant.htm), Tape Measures
TEACHER ACTIVITIES
STUDENT ACTIVITIES
Review homework and material from the
previous section.
Ask questions and give input for finding
the solutions.
Use problems #16, #17, and #18 on page
360 as a wrap up for the previous section
(these are problems about finding the
lengths and angles of right triangles.
Work on problems (in groups if desired);
and ask questions about anything that is
unclear.
Explain the concepts of angles of
elevation and angles of depression.
Listen to explanation; ask questions if
they have any.
Do example #1 on page 365 (this
problem involves finding a distance
when the height and angle of depression
are given).
Answer questions and give input for
finding the solution.
Assign ‘Checking for Understanding’
#1, #2, and #3 on page 366 (these are
practice problems involving using angles
of elevation and angles of depression).
Work on problems and ask any questions
they might have.
Hand out materials and instructions for
making quadrants (these can also be premade).
Follow instructions and make quadrants.
Take class out into hallway and instruct
them to measure various heights using
the quadrant and tape measure.
In pairs, measure angles of elevation and
horizontal distances, and record data on
a table. Use this information to compute
heights of objects.
If time allows, have a couple of students
present their measurements and
calculations.
Volunteers will present their work in
front of the class and answer any
Questions.
Hand out homework assignment, explain
it, and answer any questions.
Ask questions if they have any.
Connections to NCTM Standards:
This lesson incorporates the Geometry Standard of using trigonometric
relationships to determine lengths and angle measurements. Through the assessment, it
also includes the Measurement Standard of analyzing accuracy error in measurement
situations.
This lesson also incorporates the Problem Solving and Communication Standards.
It has students solve real life problems that arise in math and other contexts, and has them
communicate their mathematical thinking to peers and the teacher.
Accommodations:
Students who have difficulty manipulating objects can have their quadrants premade or made by another student. If there are students with serious behavioral problems,
the teacher may have to pre-cut the quadrant materials. Students with more specific
disabilities will be accommodated in a case-by-case manner.
Assessment:
Students will be assessed on their class participation and their homework
assignment. The homework assignment is a performance assessment that will measure
their ability to take what they learned in class and apply it outside of school (see
assignment).