Mathematics - Junior Secondary 2 - Angles of elevation and depression

Angles of elevation and depression

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TERM: 3RD TERM

WEEK 4
Class: Junior Secondary School 2
Age: 13 years
Duration: 40 minutes per period
Subject: Mathematics
Topic: Angles of Elevation and Depression
Focus: Use of Angles in Calculating Distances and Heights Using Scale Drawing

SPECIFIC OBJECTIVES:

By the end of the lesson, pupils should be able to:

  1. Understand the concept of the angle of elevation and depression.
  2. Use angles of elevation and depression to calculate distances and heights using scale drawing.
  3. Solve quantitative aptitude problems related to angles of elevation and depression.
  4. Apply the concepts of angles of elevation and depression in practical scenarios.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Practical illustrations
  • Problem-solving exercises
  • Scale drawing exercises

INSTRUCTIONAL MATERIALS:

  • Protractor
  • Ruler
  • Graph paper
  • Whiteboard and markers
  • Scale drawing charts
  • Pictures of real-life scenarios involving elevation and depression (e.g., buildings, hills, airplanes)

 

PERIOD 1 & 2: Understanding the Angle of Elevation and Depression

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Teacher introduces the concepts of angle of elevation and angle of depression with practical examples (e.g., standing at the base of a building looking up and vice versa).

Pupils listen and ask questions for clarity.

Step 2 - Explanation

Teacher defines and explains the angle of elevation (the angle formed when an observer looks upward) and depression (the angle formed when an observer looks downward).

Pupils observe and ask questions about the differences between both angles.

Step 3 - Demonstration

Teacher demonstrates both angles using a protractor and a drawing of a building. Teacher shows how to measure these angles with a protractor.

Pupils practice drawing their own examples with a protractor and measuring angles of elevation and depression.

Step 4 - Note Taking

Teacher writes the definitions of the angles on the board.

Pupils take notes.

NOTE ON BOARD:

  • Angle of Elevation: The angle formed when looking upward from the horizontal.
  • Angle of Depression: The angle formed when looking downward from the horizontal.

EVALUATION (5 exercises):

  1. Identify the angle of elevation in a given scenario (e.g., standing at the foot of a tree and looking up).
  2. Define angle of depression with an example.
  3. Identify whether the following situation involves an angle of elevation or depression: "Looking from the top of a hill to the bottom."
  4. Draw and label an example of both angles.
  5. Name a real-life situation where an angle of depression is used.

CLASSWORK (5 questions):

  1. Draw an angle of elevation from the base of a building to the top.
  2. Define the angle of depression.
  3. Measure the angle of elevation in a given diagram.
  4. Draw a scenario where an angle of depression occurs.
  5. Explain the use of angles of elevation in real-life applications (e.g., astronomy).

ASSIGNMENT (5 tasks):

  1. Define the angle of elevation and provide one practical example.
  2. Define the angle of depression and provide one practical example.
  3. Draw and label an angle of depression.
  4. Measure the angle of elevation in the given diagram.
  5. Write one real-life situation where both angles can be applied.

 

PERIOD 3 & 4: Using Angles of Elevation and Depression in Scale Drawing

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Teacher explains the concept of scale drawing and how it is used to calculate distances and heights in real-life situations involving elevation and depression.

Pupils listen and engage with questions.

Step 2 - Explanation

Teacher demonstrates how to use a scale drawing to solve problems involving angles of elevation and depression.

Pupils observe and take notes.

Step 3 - Demonstration

Teacher walks pupils through a problem-solving example using a scale drawing to calculate the height of a building from a given angle of elevation.

Pupils solve similar problems with teacher guidance.

Step 4 - Note Taking

Teacher provides key steps for using scale drawings to calculate heights and distances.

Pupils take notes and practice the method.

NOTE ON BOARD:

  • Scale Drawing Method:
  1. Draw a scale diagram of the situation.
  2. Label the known angles (angle of elevation or depression) and distances.
  3. Use the protractor to measure the angle and scale to measure distances.
  4. Apply trigonometric ratios (optional) or use proportional reasoning to calculate unknown distances or heights.

 

EVALUATION (5 exercises):

  1. Calculate the height of a building using a scale drawing and an angle of elevation of 30°.
  2. Draw a scale diagram showing the angle of depression of a building from a given point.
  3. Use a scale drawing to calculate the distance from a point to the top of a mountain given an angle of elevation.
  4. In a scale drawing, find the height of a tree when the angle of elevation from a point 10 meters away is 45°.
  5. Using a scale drawing, find the distance from the top of a hill to a point on the ground when the angle of depression is 60°.

CLASSWORK (5 tasks):

  1. Draw a scale diagram of a situation with an angle of elevation.
  2. Use scale drawing to measure the height of an object given the distance and angle of elevation.
  3. Calculate the distance from the top of a hill to a point 20 meters away using scale drawing.
  4. Use a scale diagram to find the angle of depression from a height of 15 meters to a point 30 meters away.
  5. Solve a problem involving the calculation of distance using a scale drawing.

ASSIGNMENT (5 tasks):

  1. Draw a scale diagram showing the angle of depression of a tower from a given point.
  2. Calculate the height of a building using a scale diagram where the angle of elevation is 45°.
  3. Use a scale drawing to calculate the distance from a plane flying at 1000 meters altitude to a point on the ground with an angle of depression of 30°.
  4. Solve a quantitative problem involving angles of elevation or depression using scale drawing.
  5. Create a word problem that involves calculating distances and heights using scale drawing.

 

PERIOD 5: Solving Quantitative Problems Involving Angles of Elevation and Depression

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Teacher explains how angles of elevation and depression can be used to solve quantitative aptitude problems involving distances, heights, and objects.

Pupils listen and ask questions.

Step 2 - Explanation

Teacher demonstrates solving a word problem involving the use of angles of elevation and depression to calculate the height of an object.

Pupils observe and solve similar problems with teacher guidance.

Step 3 - Problem Solving

Teacher presents a set of quantitative problems for pupils to solve in class. Pupils apply the knowledge learned in the previous lessons.

Pupils work in pairs or individually to solve the problems.

Step 4 - Review

Teacher reviews the solutions with the class, answering any questions.

Pupils ask clarifying questions and participate in the review.

 

EVALUATION (5 questions):

  1. A man is standing 50 meters from a tree. The angle of elevation to the top of the tree is 30°. Find the height of the tree.
  2. From the top of a hill 100 meters high, the angle of depression to a car at the base is 60°. Find the distance from the top of the hill to the car.
  3. An airplane is flying 500 meters above the ground. The angle of depression from the plane to a point on the ground is 45°. Find the distance from the plane to the point.
  4. A building casts a shadow of 100 meters when the angle of elevation of the sun is 30°. Find the height of the building.
  5. From a point on the ground, the angle of elevation to the top of a tower is 45°. If the distance from the point to the base of the tower is 20 meters, find the height of the tower.

CLASSWORK (5 tasks):

  1. Solve a problem involving the use of angles of elevation to find the height of a building.
  2. Calculate the distance from a point to the top of a mountain given the angle of elevation.
  3. Use angles of depression to solve a problem involving the height of a building and distance from the observer.
  4. Solve a word problem involving the use of angles of elevation and depression.
  5. Review and calculate the height of a tree using angles of elevation in a word problem.

ASSIGNMENT (5 tasks):

  1. Solve a problem involving the use of angles of depression to find the height of an object.
  2. Use angles of elevation to solve a real-life problem involving a building's height.
  3. Write and solve your own word problem involving angles of elevation and depression.
  4. Find the distance from a point to the top of a hill using scale drawing.

Calculate the height of a tower using angles of elevation and depression.