Calculating the Height when Angle of Elevation is Given Mathematics JSS 2 Third Term Lesson Notes Week 1

Subject: Mathematics

Class: JSS 2

Term: Third Term

Week: 1

Topic: Finding the Height of a Building using Angles

Sub-topic: Calculating height from distance and angle of elevation

Duration: 45 minutes

Behavioural Objectives:

• By the end of the lesson, students should be able to calculate the height of a building given its distance and the angle of elevation.
• Students should understand the concept of angles and height in relation to buildings.

Key words: Angle, elevation, height, distance, level ground, calculation, formula.

Entry Behaviour: Students should be able to identify different shapes and understand basic addition and subtraction.

Learning Resources and Materials:

• Chalkboard/Whiteboard
• Chalk/Markers
• Visual aids (pictures of buildings, angles)
• Ruler (for demonstrating distance)
• Calculators (for teacher demonstration)

Building Background / Connection to Prior Knowledge:

• Review basic shapes and angles.
• Discuss how buildings look from different distances and angles.

Embedded Core Skills:

• Numeracy: Using numbers to calculate height.
• Spatial awareness: Understanding the relationship between distance, angle, and height.

Learning Materials:

• Lagos State Scheme of Work for JSS 2 Mathematics
• Mathematics textbook for JSS 2

Instructional Materials:

1. Introduction of the topic
2. Demonstration of how to calculate height using distance and angle
3. Interactive activities for students to practice

Content:

The angle of elevation of the top of a building i 35° from a point 55m away on a level ground. Calculate the height of the building

1. What’s an angle?: An angle is like a corner. 📐
2. Elevation means height: It’s how high something is.
3. Point of view: It’s where you’re looking from.
4. Level ground: Ground that’s flat, like the floor in your classroom.
5. How far away?: 55 meters means it’s 55 big steps away.
6. How to find height?: We use angles and distance to find out.
7. Formula: Height = Distance x Tan(Angle).
8. Calculating step-by-step: Let’s put numbers in the formula.
9. Result: The height of the building is the answer we find. 🏢

1. Given information:
   • Angle of elevation = 35°
   • Distance from the building = 55m
2. Using the formula:
   • Height = Distance x Tan(Angle)
3. Plug in the values:
   • Height = 55m x Tan(35°)
4. Calculate Tan(35°):
   • Tan(35°) ≈ 0.7002 (you can use a calculator for this)
5. Multiply distance by Tan(35°):
   • Height ≈ 55m x 0.7002 ≈ 38.511 meters
6. Result:
   • The height of the building is approximately 38.511 meters.

Evaluation :

1. The angle of ________ helps us find the height of a building.
   • a) distance
   • b) elevation
   • c) shape
   • d) color
2. When you look up at a tall building, you are looking at its ________.
   • a) width
   • b) length
   • c) height
   • d) depth
3. To find the height of a building, we need to know the ________ and the angle of ________.
   • a) width, view
   • b) distance, angle
   • c) color, distance
   • d) height, width
4. If the angle of ________ is 30° and the distance is 50 meters, what is the height of the building?
   • a) view
   • b) height
   • c) elevation
   • d) width
5. The formula to calculate height is ________ = Distance x Tan(Angle).
   • a) Height
   • b) Width
   • c) Length
   • d) Depth
6. Tan(35°) is approximately ________.
   • a) 0.500
   • b) 0.700
   • c) 0.900
   • d) 1.200
7. The distance from the building is usually measured in ________.
   • a) steps
   • b) meters
   • c) centimeters
   • d) kilometers
8. The angle of elevation helps us understand how ________ the building is from where we stand.
   • a) tall
   • b) short
   • c) wide
   • d) colorful
9. We use a ________ to calculate Tan(35°).
   • a) ruler
   • b) calculator
   • c) pencil
   • d) eraser
10. The ground where we stand should be ________ for accurate measurements.
    • a) flat
    • b) bumpy
    • c) wet
    • d) sandy
11. If the angle of ________ is 45° and the distance is 60 meters, what is the height of the building?
    • a) height
    • b) view
    • c) elevation
    • d) width
12. Knowing the height of a building helps architects and engineers with ________.
    • a) drawing pictures
    • b) building bridges
    • c) making cakes
    • d) planting trees
13. Tan(40°) is approximately ________.
    • a) 0.700
    • b) 0.800
    • c) 0.900
    • d) 1.000
14. We use the formula Height = Distance x ________ to find the height of a building.
    • a) Angle
    • b) Length
    • c) Tan(Angle)
    • d) Width
15. The height of a building is measured from its ________ to the top.
    • a) base
    • b) middle
    • c) roof
    • d) window

Class Activity Discussion :

1. What does the angle of elevation mean?
   • Answer: It’s the angle we look up at something, like a tall building.
2. How do we find the height of a building?
   • Answer: We use the angle of elevation and the distance from the building.
3. Why is it important to know the height of a building?
   • Answer: It helps architects and engineers plan and build safely.
4. What is Tan(35°)?
   • Answer: It’s a math trick we use to find the height of the building.
5. How do we measure the distance from a building?
   • Answer: We use a ruler or count big steps.
6. Can we measure the height of a building without knowing the distance?
   • Answer: No, we need both distance and angle to find the height.
7. What happens if the ground is not flat?
   • Answer: We might get the wrong height, so it’s important to stand on flat ground.
8. What if the angle of elevation is 90°?
   • Answer: That means we’re looking straight up, and the building’s height is the same as the distance.
9. How can I practice finding building heights?
   • Answer: You can use toy buildings and pretend to measure them.
10. Why do we need to learn about angles and height?
    • Answer: It helps us understand how tall things are and how to measure them.
11. What if I don’t have a calculator to find Tan(35°)?
    • Answer: You can ask someone who has one or use a calculator app on a phone or computer.
12. Can we measure the height of anything using angles?
    • Answer: Yes, we can use angles to find the height of trees, mountains, and even people!
13. Why do we need to measure the height of buildings?
    • Answer: It helps us know if buildings are safe and if they fit in with other buildings nearby.
14. What if the angle of elevation is smaller than 90°?
    • Answer: That’s normal! Most of the time, we look up at things from an angle.
15. Is it easy to find the height of a building?
    • Answer: With practice and using the right formula, it can become easy and fun!

simpler explanation:

1. Angle: Imagine looking up at the top of a building. The angle you look up is 35°.
2. Distance: You’re standing 55 meters away from the building.
3. Level ground: The ground you’re standing on is flat.
4. Height formula: We use a special math rule to find the height.
5. Tan(35°): This is a math trick we use to find the height. It’s like a secret code.
6. Multiply: We take the distance (55m) and multiply it by the secret code.
7. Result: The answer we get is the height of the building. 🏢

Example:

• Angle: 35°
• Distance: 55m
• Tan(35°) ≈ 0.7002
• Height ≈ 55m x 0.7002 ≈ 38.511 meters

So, the height of the building is approximately 38.511 meters.

More Examples :

Example 1:

• Angle: 35°
• Distance: 55m
• Formula: Height = Distance x Tan(Angle)
• Tan(35°) ≈ 0.7002
• Height ≈ 55m x 0.7002 ≈ 38.511 meters

Example 2:

• Angle: 40°
• Distance: 60m
• Formula: Height = Distance x Tan(Angle)
• Tan(40°) ≈ 0.8391
• Height ≈ 60m x 0.8391 ≈ 50.346 meters

Example 3:

• Angle: 25°
• Distance: 70m
• Formula: Height = Distance x Tan(Angle)
• Tan(25°) ≈ 0.4663
• Height ≈ 70m x 0.4663 ≈ 32.641 meters

Example 4:

• Angle: 45°
• Distance: 50m
• Formula: Height = Distance x Tan(Angle)
• Tan(45°) = 1 (since Tan(45°) = 1)
• Height = 50m x 1 = 50 meters

Example 5:

• Angle: 30°
• Distance: 45m
• Formula: Height = Distance x Tan(Angle)
• Tan(30°) ≈ 0.5774
• Height ≈ 45m x 0.5774 ≈ 26.007 meters

These examples show how to find the height of different buildings using angles and distances.

Content:

1. Revision: The teacher revises the previous topic on basic shapes and angles.
2. Introduction: The teacher introduces the new topic of finding the height of a building using angles.
3. Discussion: Students are encouraged to share their ideas about how tall buildings are measured and what angles have to do with it.
4. Explanation: The teacher explains the concept of angle of elevation and how it helps us calculate the height of a building.
5. Demonstration: Using visual aids and a ruler, the teacher demonstrates how to calculate height using distance and angle.
6. Practice: Students are given examples to solve on their own, with guidance from the teacher.
7. Assessment: The teacher evaluates students’ understanding through questioning and observation.
8. Conclusion: The teacher wraps up the lesson by summarizing the key points and providing feedback to students.

Presentation:

• The teacher uses simple language and visual aids to explain the concept.
• Students are encouraged to ask questions and participate in discussions.

Step 1: The teacher revises the previous topic which was about shapes and angles. Step 2: The teacher introduces the new topic of finding the height of a building using angles. Step 3: The teacher allows the pupils to give their own contributions and corrects them when necessary.

Teacher’s Activities:

• Presenting the lesson
• Demonstrating calculations
• Guiding students in practice exercises
• Providing feedback and assessment

Learners’ Activities:

• Listening to the teacher’s explanation
• Participating in discussions
• Solving practice problems individually or in groups

Assessment:

• Observing students’ participation and understanding during the lesson
• Asking questions related to the topic to assess comprehension

Evaluation Questions:

1. What is an angle?
2. What does elevation mean?
3. How do we measure the height of a building?
4. Can you name a tool we use to measure distance?
5. What is the formula for calculating height from distance and angle?
6. If the angle of elevation is 40° and the distance is 60m, what is the height of the building?
7. How can we use angles to find the height of things?
8. Why is it important to know the height of a building?
9. How do we know if the ground is level?
10. Can you explain how angles help us understand height better?

Conclusion:

• The teacher goes around to mark students’ work and provide necessary feedback on the topic.