What is the smallest interior angle of triangle ABC?

  • Thread starter Thread starter ~Sam~
  • Start date Start date
  • Tags Tags
    Angle Interior
Click For Summary
SUMMARY

The smallest interior angle of triangle ABC, with vertices A = (3,1,-2), B = (3,0,-1), and C = (5,2,-1), can be determined using the cosine law or the dot product method. The cosine law provides a straightforward approach to calculate angles between line segments AB, BC, and AC. The discussion emphasizes the importance of calculating angles between two pairs of line segments to find the smallest angle effectively.

PREREQUISITES
  • Understanding of vector operations, specifically dot product
  • Familiarity with the cosine law in triangle geometry
  • Basic knowledge of 3D coordinate systems
  • Ability to perform calculations involving angles and lengths
NEXT STEPS
  • Study the cosine law for triangle angle calculations
  • Learn vector dot product calculations in 3D space
  • Explore methods for determining angles in triangles using coordinate geometry
  • Practice solving problems involving interior angles of triangles
USEFUL FOR

Students studying geometry, particularly those focused on triangle properties and angle calculations, as well as educators looking for effective teaching methods in vector mathematics.

~Sam~
Messages
70
Reaction score
0

Homework Statement


Find the smallest interior angle of the triangle ABC whose vertices are given.
A = (3,1,-2), B = (3,0,-1), C = (5,2,-1)



Homework Equations



I think the equation arccos( U dot V / (lengthU)(lengthV)

The Attempt at a Solution



What i did is tried the formula for all combinatations: AB, BC, AC to get all the angles, and which ever was the smallest I choose. Unfortunately I do not get the correct answer.
 
Physics news on Phys.org
Show us what you did. You only need to find the angles between two pairs of line segments. Once you know two of the angles, you can find the third pretty easily.
 
All most the same thing but instead of using the dot product you could use the "cosine law" to find the angles.
 

Similar threads

Replies
3
Views
2K
  • · Replies 19 ·
Replies
19
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
3
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
Replies
12
Views
3K
Replies
5
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K