What is the smallest interior angle of triangle ABC?

In summary, to find the smallest interior angle of triangle ABC, which has vertices at A=(3,1,-2), B=(3,0,-1), and C=(5,2,-1), one can use the equation arccos(U dot V / (lengthU)(lengthV)), where U and V are two line segments of the triangle. Alternatively, the "cosine law" can also be used to find the angles.
  • #1
~Sam~
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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.
 
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  • #2
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.
 
  • #3
All most the same thing but instead of using the dot product you could use the "cosine law" to find the angles.
 

1. What is the smallest interior angle in a polygon?

The smallest interior angle in a polygon is always less than 180 degrees, as a polygon cannot have an angle greater than 180 degrees.

2. How do you find the smallest interior angle in a triangle?

The smallest interior angle in a triangle can be found by dividing 180 degrees by the number of angles in a triangle, which is 3. Therefore, the smallest interior angle in a triangle is always 60 degrees.

3. Is the smallest interior angle in a regular polygon always the same?

Yes, in a regular polygon, all interior angles are equal. Therefore, the smallest interior angle in a regular polygon will always be the same, regardless of the number of sides.

4. Can the smallest interior angle in a polygon be negative?

No, the smallest interior angle in a polygon cannot be negative. It will always be a positive value, as angles in a polygon are measured in degrees, which are always positive.

5. How does the number of sides in a polygon affect the size of the smallest interior angle?

The number of sides in a polygon does not affect the size of the smallest interior angle. The size of the smallest interior angle is determined by the formula (180(n-2))/n, where n is the number of sides in the polygon. As long as the number of sides is greater than 2, the smallest interior angle will always be less than 180 degrees.

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