UTPA STEM/CBI Courses/Calculus/Solving Right Triangles

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Course Title: PreCalculus (Math 2412)

Lecture Topic: Solving Right Triangles

Instructor: Lily Rai

Institution: South Texas College

Backwards Design[edit]

Course Objectives

  • Primary Objectives- By the end of the next class period students will be able to:
    • Solve application problems involving angles of elevation, angles of depression and bearing.
  • Sub Objectives- The objectives will require that students be able to:
    • Identify angles in standard position, co-terminal angles and reference angles.
    • Define trigonometric functions using right triangles.
    • Explain angles of elevation, angles of depression and bearing.
  • Difficulties-
    • Some students may face difficulty in distinguishing between angles in standard position, reference angles and co-terminal angles.
    • Many students will have difficulty in understanding the word problems and translating them into mathematical equations.
  • Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
    • There are many real life applications. One of them is the design of highway curves where outside of a curve is often slightly elevated or inclined above the inside of the curve. This inclination is called Super-elevation.
    • Another application is finding the minimum distance of a plant from a fence which requires full sun during winter.
    • Calculating the distance between two cities or two ships, or the distance flown by a plane.
    • Measuring the height of buildings, length of shadows, height of an antenna etc.

Model of Knowledge

  • Concept Map
    • Understand angles in standard position, reference angles and co-terminal angles
    • Define Trigonometric Functions using Right triangles
    • Solve right triangles given: angle and side, two sides
    • Find angle of elevation when lengths are known
    • Solve problems involving bearing angles of elevation and depression
  • Content Priorities
    • Enduring Understanding
      • Solving right triangles given different conditions
    • Important to Do and Know
      • Given an application problem, understand, sketch, analyze, solve, and check for correctness.
    • Worth Being Familiar with
      • Pythagorean Theorem, Bearing: a concept in navigation; angles of elevation and depression
      • Calculating distance between any two points given the coordinates
      • To find the length of an arc; to measure the area of a sector

Assessment of Learning

  • Formative Assessment
    • In Class (groups)
      • Students to work in groups on selected application problems and present it to the entire class
    • Homework (individual)
      • Students will work on assigned problems and bring the difficulties to the next class
  • Summative Assessment
    • In class quiz over the lesson

Legacy Cycle[edit]

OBJECTIVE

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

  • Differentiate between angles in standard position, co-terminal angles, and reference angles
  • Solve the right triangle given an angle or a side or two sides
  • Solve application problems involving bearing, and angles of elevation and depression

The objectives will require that students be able to:

  • Recognize a word problem as an application problem involving right triangle trigonometry
  • Solve application problems involving bearing, angles of elevation and depression, and area of a sector

THE CHALLENGE

The students will be presented with the following problem: "When an automobile travels around a curve on a highway, objects like trees, buildings and fences situated on the curve may obstruct a driver's vision. How far inside the curve of some land must be cleared to provide visibility for a safe stopping distance?"

GENERATE IDEAS

Students will be given a few minutes to individually write down their answers to the questions. Students may respond with answers as: 1) Need to know the arc length of the curve and also the area of the sector 2) Need to know the central angle and radius 3) Speed limit posted, speed of the vehicle etc. 4) Need to come up with the formula for the distance

MULTIPLE PERSPECTIVES

The Faculty will review the concepts of length of an arc, area of a sector; and then will introduce the concepts of trigonometric functions using right triangles.

RESEARCH & REVISE

Students would be provided with the actual questions on modeling highway curves and stopping distance. Students will work in groups.

TEST YOUR METTLE

The groups will make presentations to the class and will receive the feedback. The Faculty will give the correct analysis and steps to solve the problem. Students will be presented with a quiz at the beginning of the following class.

GO PUBLIC

Students will be able to answer similar questions presented at the beginning of the lesson and would be asked to turn in a brief write up.