UTPA STEM/CBI Courses/Calculus/Right Triangles: Applications

Course Title: Pre-Calculus

Lecture Topic: Right Triangle: Applications

Instructor: Jacob Makaya

Institution: TAMIU

Backwards Design

Course Objectives

• Primary Objectives- By the next class period students will be able to:
  • Solve application problems involving right triangles, angles of elevation, and angles of depression.

• Sub Objectives- The objectives will require that students be able to:
  • Define trigonometric functions using right triangles.

• Difficulties- Students may have difficulty:
  • Applying trigonometric functions to real-world problems.
  • Visualizing real-world problems and translating them into equations.

• Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
  • Solve application problems using right triangles. For example, finding distance from one point to another point. i.e. distance between building or cities., distance flown by an airplane.
  • Measure the height of towers and buildings.

Model of Knowledge

• Concept Map
  • Define trigonometric functions using right triangles.
  • Solve right triangles given one side and the angle of elevation or the angle of depression.
  • Solve real-world problems involving angles of elevation and angles of depression.

• Content Priorities
  • Enduring Understanding
    • Solving right triangles using trigonometric functions.
  • Important to Do and Know
    • Translate real-world problems into geometric figures involving right triangles.
    • Analyze problems and translate them into mathematical equations.
  • Worth Being Familiar with
    • Understand how to solve problems that involve more than one right triangle.

Assessment of Learning

• Formative Assessment
  • In Class (groups)
    • Give an application problem and have students work in groups and then share with the class.
  • Homework (individual)
    • Give a homework assignment to students.
• Summative Assessment
  • In class exam over the lesson.
  • Invite students to solve challenging problems on the board over the lesson for extra credits.

Legacy Cycle

OBJECTIVE

By the next class period, students will be able to:

• Solve right triangles using trigonometric functions.
• Apply right triangle to solve real-world problems involving angles of elevation and angles of depression.

The objectives will require that students be able to:

• Identify problems that require right triangles and determine what trigonometric functions to use.

THE CHALLENGE

You are applying for a job to become a professional photographer in a company. In the interview, are asked to take only one full picture of John, who is 6 feet tall. A camera is mounted on a tripod 4 feet high at a distance of 10 feet from John. If the camera lens has angles of depression and elevation of 20 degrees, will you take the picture? If not, how far back should you move the camera to include John’s feet and head?

GENERATE IDEAS

How would students be able to answer this problem? Some of the ideas students may bring are:

• What will be the maximum height of a picture for the given angles?
• If the maximum height is less than 6 feet, what distance should the camera be moved so that the maximum height of the picture is 6 feet?

MULTIPLE PERSPECTIVES

Students work for a few minutes and come up with ideas. Then the instructor provides the concept of right triangles, angles of depression and elevation.

RESEARCH & REVISE

After the students understand the geometric figure the instructor explains how trigonometric functions and right triangles can be used to solve the problem. Students will have to decide particular functions to use.

TEST YOUR METTLE

Each group will present their answer to the class. The instructor will provide feedbacks on how to analyze and solve the problems.

GO PUBLIC

Students will be asked to find similar problems and solve them in front of the class.

Pre-Lesson Quiz

(See Extra Credit under Summative Assessment.)

Test Your Mettle Quiz

1. A person in a small boat, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be 25 degrees, how far offshore is the boat?

2. A 22-foot extension ladder leaning against a building makes a 70-degree angle with the ground. How far up the building does the ladder touch?

3. A state trooper is hidden from 30 feet from a highway. One second after a truck passes the angle theta between the highway and the line of observation from the patrol car to the truck is measured. If the angle measures 15 degrees, how fast is truck traveling? Express the answer in miles per hour.

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