# Deceiving Simple Geometry Question

• hobbes33
In summary, the conversation is about a geometry question that involves finding the value of BC. It is mentioned that there is a unique answer for BC according to scale models. However, using equations with Pythagoras' theorem or cosine rule seems to result in a confusing mess. The person asks if anyone has any other ideas for solving the question. Another person points out that there are 7 unknown angles and 7 equations to relate them, making the solution unique. They suggest using trigonometry to find BC. However, another person doubts that there is a simpler way to solve the question without solving a 7 variable simultaneous equation. They mention finding a solution using the Law of Sines but later realize their drawing was incorrect. A software is
hobbes33

Here's a simple looking geometry question, but I can't seem to solve it.
But according to scale models, there is a unique answer for BC.

Equations with Pythagoras' theorem or cosine rule always seems to end up in an illegible pile of mess.

Does anyone has any idea how to go about solving the question?

You have 7 unknown angles and there are 7 linear independent equations relating them, so the solution is unique. You can use the angles and trigonometry to find BC.

Thanks for pointing out that info.

But isn't there another way to solve this question rather than to solve a 7 variable simultaneous equation? Most variables are not linear combination of each other too, so I doubt the 7 equations are practically reducible.

I was able to find a solution using the Law of Sines on triangle AYX, namely on angles AYX and YAX

edit:
nevermind, i drew the picture incorrectly.

Last edited:
In case anyone wants to check, the answer should be around 3.6 using a scale model.

By using a software to digest some of the equations i threw in, the answer comes out to approximately 3.580181.

But of course, the equations are too long for someone to solve by hand. I think someone must have a better method than me.

## 1. What is a deceiving simple geometry question?

A deceiving simple geometry question is a question that appears easy at first glance, but actually requires a more complex understanding of geometry concepts to solve. These questions often involve tricky wording, hidden assumptions, or visual illusions that can lead to incorrect answers if not carefully considered.

## 2. How can I recognize a deceiving simple geometry question?

There are a few key things to look out for when trying to identify a deceiving simple geometry question. These include vague or misleading wording, visual elements that may distort the perception of shapes or angles, and questions that seem too easy or straightforward compared to the rest of the questions on a test or assignment.

## 3. What strategies can I use to solve a deceiving simple geometry question?

The best strategy for solving a deceiving simple geometry question is to carefully read and analyze the question to identify any potential traps or hidden assumptions. It can also be helpful to draw a diagram or use visual aids to better understand the problem. Additionally, double checking your work and considering alternative solutions can help catch any mistakes or misunderstandings.

## 4. Why are deceiving simple geometry questions important?

Deceiving simple geometry questions can be important for building critical thinking skills and testing a student's ability to apply their knowledge in unexpected ways. They can also help identify areas where a student may need to improve their understanding of geometry concepts.

## 5. Are there any real-life applications for deceiving simple geometry questions?

Deceiving simple geometry questions can be found in many aspects of everyday life, such as in architecture, design, and engineering. Being able to identify and solve these types of questions can be useful in problem-solving and decision-making in various career fields.

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