Stuck on the sides of a triangle problem

In summary, the conversation is about finding the values for the sides and angle of a triangle using the Pythagorean Theorem and the Geometric Mean Theorem. The problem involves two right triangles and three unknown variables. The final question is whether the angle between sides a and b is 90 degrees.
  • #1
tony700
5
0
I have figured out the triangle's height and base, but I need to figure out sides a and b. I have tried Pythagorean theorem and similar triangle ratios, but it is not working out. Please help. See picture below. Thank you.View attachment 6489
 

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  • #2
We have that two right triangles and from the Pythagorean Theorem for those two we get:
$$464^2+e^2=a^2$$ and $$464^2+(1218-e)^2=b^2$$

From the Geometric mean theorem we have that $$464^2=e\cdot (1218-e)$$

Now we have three unknown variables, $a,b,e$, and three equations. So, we can find the values for $a,b,e$.
 
  • #3
Is the angle contained by $a$ and $b$ equal to $90^\circ$? For that matter, what is the complete problem?
 

1. What is the "Stuck on the sides of a triangle problem"?

The "Stuck on the sides of a triangle problem" is a mathematical puzzle where three objects are placed on the sides of a triangle and the goal is to rearrange them so that each object is on the side opposite of where it started.

2. How do you solve the "Stuck on the sides of a triangle problem"?

The key to solving this problem is to understand the concept of rotational symmetry. By rotating the triangle, you can move the objects to their desired locations. It may take a few rotations to achieve the correct orientation.

3. Are there any specific strategies for solving this problem?

Yes, there are a few strategies that can help you solve the "Stuck on the sides of a triangle problem". One approach is to start by moving the object that is in the most difficult position first, then work your way to the easier positions. Another strategy is to try to visualize the rotations in your mind before physically moving the objects.

4. Is there a mathematical formula for solving this problem?

There is no specific mathematical formula for solving this problem, as it relies more on spatial reasoning and visualization. However, understanding rotational symmetry and the concept of opposite sides can aid in finding a solution.

5. Can this problem be applied to real-life situations?

While the "Stuck on the sides of a triangle problem" may seem like a purely mathematical puzzle, the concept of rotational symmetry can be applied to real-life situations. For example, it can be used in engineering and design to ensure symmetry and balance in structures and products.

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