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:
- Introduction of the topic
- Demonstration of how to calculate height using distance and angle
- 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
- What’s an angle?: An angle is like a corner. 📐
- Elevation means height: It’s how high something is.
- Point of view: It’s where you’re looking from.
- Level ground: Ground that’s flat, like the floor in your classroom.
- How far away?: 55 meters means it’s 55 big steps away.
- How to find height?: We use angles and distance to find out.
- Formula: Height = Distance x Tan(Angle).
- Calculating step-by-step: Let’s put numbers in the formula.
- Result: The height of the building is the answer we find. 🏢
- Given information:
- Angle of elevation = 35°
- Distance from the building = 55m
- Using the formula:
- Height = Distance x Tan(Angle)
- Plug in the values:
- Height = 55m x Tan(35°)
- Calculate Tan(35°):
- Tan(35°) ≈ 0.7002 (you can use a calculator for this)
- Multiply distance by Tan(35°):
- Height ≈ 55m x 0.7002 ≈ 38.511 meters
- Result:
- The height of the building is approximately 38.511 meters.
Evaluation :
- The angle of ________ helps us find the height of a building.
- a) distance
- b) elevation
- c) shape
- d) color
- When you look up at a tall building, you are looking at its ________.
- a) width
- b) length
- c) height
- d) depth
- 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
- 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
- The formula to calculate height is ________ = Distance x Tan(Angle).
- a) Height
- b) Width
- c) Length
- d) Depth
- Tan(35°) is approximately ________.
- a) 0.500
- b) 0.700
- c) 0.900
- d) 1.200
- The distance from the building is usually measured in ________.
- a) steps
- b) meters
- c) centimeters
- d) kilometers
- The angle of elevation helps us understand how ________ the building is from where we stand.
- a) tall
- b) short
- c) wide
- d) colorful
- We use a ________ to calculate Tan(35°).
- a) ruler
- b) calculator
- c) pencil
- d) eraser
- The ground where we stand should be ________ for accurate measurements.
- a) flat
- b) bumpy
- c) wet
- d) sandy
- 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
- Knowing the height of a building helps architects and engineers with ________.
- a) drawing pictures
- b) building bridges
- c) making cakes
- d) planting trees
- Tan(40°) is approximately ________.
- a) 0.700
- b) 0.800
- c) 0.900
- d) 1.000
- We use the formula Height = Distance x ________ to find the height of a building.
- a) Angle
- b) Length
- c) Tan(Angle)
- d) Width
- The height of a building is measured from its ________ to the top.
- a) base
- b) middle
- c) roof
- d) window
Class Activity Discussion :
- What does the angle of elevation mean?
- Answer: It’s the angle we look up at something, like a tall building.
- How do we find the height of a building?
- Answer: We use the angle of elevation and the distance from the building.
- Why is it important to know the height of a building?
- Answer: It helps architects and engineers plan and build safely.
- What is Tan(35°)?
- Answer: It’s a math trick we use to find the height of the building.
- How do we measure the distance from a building?
- Answer: We use a ruler or count big steps.
- Can we measure the height of a building without knowing the distance?
- Answer: No, we need both distance and angle to find the height.
- What happens if the ground is not flat?
- Answer: We might get the wrong height, so it’s important to stand on flat ground.
- 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.
- How can I practice finding building heights?
- Answer: You can use toy buildings and pretend to measure them.
- Why do we need to learn about angles and height?
- Answer: It helps us understand how tall things are and how to measure them.
- 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.
- 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!
- 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.
- 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.
- 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:
- Angle: Imagine looking up at the top of a building. The angle you look up is 35°.
- Distance: You’re standing 55 meters away from the building.
- Level ground: The ground you’re standing on is flat.
- Height formula: We use a special math rule to find the height.
- Tan(35°): This is a math trick we use to find the height. It’s like a secret code.
- Multiply: We take the distance (55m) and multiply it by the secret code.
- 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:
- Revision: The teacher revises the previous topic on basic shapes and angles.
- Introduction: The teacher introduces the new topic of finding the height of a building using angles.
- Discussion: Students are encouraged to share their ideas about how tall buildings are measured and what angles have to do with it.
- Explanation: The teacher explains the concept of angle of elevation and how it helps us calculate the height of a building.
- Demonstration: Using visual aids and a ruler, the teacher demonstrates how to calculate height using distance and angle.
- Practice: Students are given examples to solve on their own, with guidance from the teacher.
- Assessment: The teacher evaluates students’ understanding through questioning and observation.
- 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:
- What is an angle?
- What does elevation mean?
- How do we measure the height of a building?
- Can you name a tool we use to measure distance?
- What is the formula for calculating height from distance and angle?
- If the angle of elevation is 40° and the distance is 60m, what is the height of the building?
- How can we use angles to find the height of things?
- Why is it important to know the height of a building?
- How do we know if the ground is level?
- 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.