# 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.

**E****valuation** :

- 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.