How do I solve triangles in 3D with specific vertices?

In summary, the problem is finding the angles in a triangle with vertices at [2,-1,0], [5,-4,3], and [1,-3,2]. The angle between two vectors can be found using the dot product and the formula |u||v|cos{\theta}. However, the sum of the three angles only equals 110, not 180. Another approach is to use the distance between points to find the lengths of the triangle, then apply the cosine rule. It's important to consider the direction of the vectors and the angle between them.
  • #1
uf2010
2
0
How do i find the angles in the triangle with the vertices at [2,-1,0], [5,-4,3], and [1,-3,2]. This problem has been bothering me because when i find the angle between the vectors it only adds to roughly 110 degrees, and that cannot be right.
 
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  • #2
To find the angle between two vectors you can use

[tex]u\cdot v=|u||v|\cos{\theta}[/tex]
 
  • #3
I have tried this, but the sum of the three angles only equals 110 not 180.
 
  • #4
nicksauce's approach should work here. You should be careful of the directions the vectors point and the angle between them. The angle between the tail of a vector and and the head of another vector is not the same as the one given by the dot product.
 
  • #5
Another way which doesn't involve vectors would be to find the lengths of the triangle by calculating distance between points, then apply cosine rule. A purely geometrical approach.
 

What is a 3D triangle?

A 3D triangle is a three-dimensional shape with three sides and three corners, also known as vertices. It is a flat surface that exists in three-dimensional space.

How do you solve a 3D triangle?

To solve a 3D triangle, you need to know the length of at least three sides or angles. You can use trigonometric ratios, such as sine, cosine, and tangent, to calculate missing sides or angles. You can also use the Pythagorean theorem to find the length of the missing side in a right triangle.

What is the difference between a 3D triangle and a 2D triangle?

The main difference between a 3D triangle and a 2D triangle is the dimension in which they exist. A 3D triangle has three dimensions - length, width, and height, while a 2D triangle only has two dimensions - length and width. Additionally, a 3D triangle can have different shapes, such as equilateral, isosceles, or scalene, while a 2D triangle can only be one of these three types.

What are some real-world applications of solving 3D triangles?

Solving 3D triangles is essential in various fields such as architecture, engineering, and physics. It is used to calculate the dimensions of buildings, bridges, and other structures. It also helps in navigation and surveying, as well as in designing 3D models and animations.

What are some challenges in solving 3D triangles?

One of the main challenges in solving 3D triangles is visualizing the shape in three dimensions. It can be challenging to accurately measure and calculate angles and sides without proper tools. Additionally, dealing with more than three sides or angles in a 3D triangle can make the calculations more complex.

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