Lesson 6: Longitudes and Latitudes

👨🏽‍🏫 Introduction

Have you ever used Google Maps or tracked a plane’s route? Or maybe seen coordinates like “5°N, 0°”? Those numbers describe locations using latitude and longitude — a global grid system that helps us navigate the Earth. 🌍

In this lesson, you’ll learn how to calculate distance between points on the Earth using latitude and longitude — especially on the same meridian or parallel. You’ll also understand the meaning of great circles and how Earth is measured using angles.

• 🌐 Understand latitude and longitude
• 📏 Calculate distances along meridians and the equator
• 🧭 Use angular measurements (degrees and minutes)

🧠 Key Concepts

📌 1. Latitude and Longitude

• Latitude: Horizontal lines from 0° at the equator to 90° North or South.
• Longitude: Vertical lines from 0° at the Prime Meridian to 180° East or West.
• Measured in degrees (°) and minutes (‘), where .

📐 2. Important Circles

• Equator: 0° latitude — the longest parallel (great circle)
• Prime Meridian: 0° longitude — passes through Greenwich, London
• Great Circle: Any circle that divides the Earth into two equal halves — used in shortest air or sea routes.

📏 3. Distance on Earth’s Surface

• Earth’s radius ≈
• Circumference ≈
• Distance for 1° of arc ≈ 111 km

📏 4. Distance Formula Along a Circle

To find the distance between two points along the same latitude or longitude:

• Along longitude: Use angular difference in latitude × 111 km
• Along equator or same latitude:
  

🔍 Worked Examples

1. 1. Example 1: Find the distance between 10°N and 25°N along the same meridian.

      Difference =
      Distance =
      🟢 Distance is 1665 km.

1. 1. Example 2: Find the distance between 20°E and 50°E along the equator.

      Difference =
      Since it’s on the equator, cos(latitude) = 1
      Distance =
      🟢 Distance = 3330 km.

1. Example 3: Find the distance between 20°W and 35°E along 10°N.

   Angular difference =
   Distance =
   🟢 Distance ≈ 6005.18 km.

✍🏽 Practice Exercises

🅰️ Section A – Along Longitude (Same Meridian)

1. Find the distance from 12°S to 48°S.
2. Find the distance between 3°N and 33°N.

🅱️ Section B – Along Latitude (Same Parallel)

1. Find the distance between 25°W and 35°E along the equator.
2. Find the distance between 15°W and 45°E along 20°N.

✅ Answers and Explanations

• A1: Difference = → Distance =
• A2: Difference = → Distance =
• B1: Total difference = → Distance =
• B2: Difference =
  Cos(20°) ≈ 0.94
  Distance =

📌 Recap

• ✅ Use latitude and longitude to locate and measure distance on Earth
• ✅ 1° of arc is about 111 km along a great circle
• ✅ Use cosine of latitude for east-west distances along parallels

💭 Reflection Prompt

Try finding your current coordinates online. Can you calculate the distance from your location to another city using what you’ve learned? How close is your answer to the real-world flight distance?