By Shahabuddin Amerudin
Introduction
Imagine embarking on a quirky adventure, where you’re on a mission to locate a peculiar parking spot – the place where a Blue Beetle car is casually chilling near a highway. Our goal? To uncover the coordinates of this enigmatic spot. But fret not, this quest is not to be taken too seriously. We’re about to explore how a bit of math and a touch of imagination can lead us to the destination of a classic car adventure.
Setting the Stage
In the charming world of automotive enthusiasts, the Blue Beetle car is no stranger. Renowned for its distinct charm and vibrant blue color, the Blue Beetle is often associated with leisurely drives and fun outings. And, well, what’s more leisurely than parking by a highway, soaking in the views, and creating a mini roadside spectacle?
The Challenge
Our adventure begins with a puzzle. We’re handed two sets of clues:
- Clue 1: The Blue Beetle is located near a highway somewhere in Saudi Arabia, I guess.
- Clue 2: We’re given the coordinates of two cities – Mecca and Medina, but with a twist. Mecca is represented as ‘B’ (21.3891° N, 39.8579° E), and Medina is represented as ‘C’ (24.5246° N, 39.5693° E).
Our mission? To triangulate and find the elusive spot ‘A’ – the coordinates where the Blue Beetle is having its highway rendezvous.
The Math Behind the Madness
Now, before you break into a cold sweat thinking about algebraic equations, don’t worry! We’re going to use some simple trigonometry and a sprinkle of geography to solve this puzzle.
First, we need to account for the distances. We’re given that the Blue Beetle is 935 km away from Mecca (‘B’) and 939 km from Medina (‘C’). However, our earth is not flat, and this means we need to convert these distances into angles (in radians) for our calculations.
After the conversion, we apply the haversine formula to calculate the initial bearings from ‘B’ to ‘A’ and from ‘C’ to ‘A.’ These bearings will help us pinpoint our destination.
The Reveal
Let’s break down the calculations that led us to the coordinates of point ‘A’ – the spot where the Blue Beetle is parked by the highway.
1. Converting Distances to Radians:
First, we start with the given distances:
- A-B distance: 935 km
- A-C distance: 939 km
To work with these distances on the Earth’s surface, we need to convert them into radians. We do this by dividing each distance by the Earth’s radius, which is approximately 6,371 kilometers.
A-B distance in radians = 935 km / 6371 km ≈ 0.146897 radians A-C distance in radians = 939 km / 6371 km ≈ 0.147581 radians
2. Calculating Central Angles:
The next step involves using the haversine formula to calculate the central angles between points ‘A’ and ‘B’ (central_angle_BA) and between points ‘A’ and ‘C’ (central_angle_CA).
The haversine formula involves the use of the haversine function, which is defined as:
haversine(θ) = sin²(θ/2)
Where θ is the central angle. Using this formula, we calculate the haversine of half the central angles for both A-B and A-C:
a = sin²((A-C) / 2) b = sin²((A-B) / 2)
Now, we can calculate the central angles:
central_angle_BA = 2 * atan2(sqrt(b), sqrt(1 – b)) central_angle_CA = 2 * atan2(sqrt(a), sqrt(1 – a))
3. Finding Initial Bearings (Azimuths):
With the central angles in hand, we can determine the initial bearings (azimuths) from ‘B’ to ‘A’ and from ‘C’ to ‘A’. These bearings represent the angles from the north direction to these points.
To calculate the azimuths, we use the following formulas:
Azimuth from B to A: azimuth_BA = atan2(sin(central_angle_BA), cos(central_angle_BA))
Azimuth from C to A: azimuth_CA = atan2(sin(central_angle_CA), cos(central_angle_CA))
4. Converting B and C to Radians:
Before we proceed to find the coordinates of point ‘A’, we need to convert the given coordinates of Mecca (B) and Medina (C) from degrees to radians:
B (in radians): Latitude 21.3891° N, Longitude 39.8579° E
C (in radians): Latitude 24.5246° N, Longitude 39.5693° E
5. Calculating Coordinates of A:
Now that we have all the necessary information, we can compute the coordinates of point ‘A’:
- Latitude of A: latitude_A = asin(sin(latitude_B) * cos(azimuth_BA) + sin(latitude_C) * cos(azimuth_CA))
- Longitude of A: longitude_A = longitude_B + atan2(sin(azimuth_BA) * cos(latitude_B), cos(azimuth_CA) – sin(latitude_B) * sin(latitude_A))
After plugging in the values, we find:
latitude_A ≈ 0.406153 radians (approximately 23.31099 degrees)
longitude_A ≈ 0.849852 radians (approximately 48.69863 degrees)
Discussion
After some nifty calculations, we’ve got our answer! The coordinates of point ‘A’ are approximately 23.31099° N and 48.69863° E. We’ve pinpointed the parking spot of our Blue Beetle, as depicted on the map below. It’s situated at the intersection of two circles, marked as I2. Point I1 is not a feasible option as it is located in Africa. To reach Mecca and Medina, one would need to cross the Red Sea or embark on an exceptionally long journey.
Nonetheless, it’s crucial to emphasize that these calculations are based on straight-line radial distances and might not provide an exact representation of real on-road travel distances. When cross-referenced with Google Maps, the most favorable estimation for the blue car’s location points to Al-Kharj, Saudi Arabia. However, it’s essential to remember that this remains a conjecture; only the car’s owner or the photographer possesses precise knowledge of its whereabouts.
Conclusion
In this light-hearted adventure, we set out to solve the mystery of the Blue Beetle’s parking spot near a highway. Through a bit of math and geographical know-how, we successfully uncovered the elusive coordinates of point ‘A’. It’s not about the seriousness of the quest; it’s about the joy of the journey, the thrill of discovery, and the whimsical world of automotive adventures.
So, next time you spot a vibrant Blue Beetle by the highway, remember the charming quest that led us to its coordinates. And perhaps, in the spirit of adventure, you can take a moment to appreciate the fun and curiosity that drive us to explore the world around us, one quirky adventure at a time!
Suggestion for Citation: Amerudin, S. (2023). A Light-hearted Quest to Locate the Elusive Parking Spot of a Blue Beetle Car. [Online] Available at: https://people.utm.my/shahabuddin/?p=7175 (Accessed: 25 September 2023).
