Trig Problem need someone to explain this

  • Context: High School 
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SUMMARY

Given two angles of a triangle, only one unique triangle can be formed because the third angle is determined by the requirement that the sum of the angles equals 180 degrees. However, if the lengths of the sides are considered, an infinite number of similar triangles can be created by scaling the triangle up or down while maintaining the same shape. The discussion highlights the concept of similar triangles and notes that when provided with two sides and a non-included angle, two distinct triangles can be formed if the non-included angle is less than 90 degrees.

PREREQUISITES
  • Understanding of basic triangle properties, specifically the angle sum property.
  • Familiarity with the concept of similar triangles.
  • Knowledge of triangle side relationships, including the Side-Angle-Side (SAS) theorem.
  • Basic trigonometry, particularly regarding angles and their measures.
NEXT STEPS
  • Study the properties of similar triangles and their applications in geometry.
  • Learn about the Side-Angle-Side (SAS) theorem and its implications for triangle construction.
  • Explore the concept of triangle congruence and the conditions under which triangles are congruent.
  • Investigate the implications of the Law of Sines and the Law of Cosines in triangle problems.
USEFUL FOR

Students studying geometry, educators teaching triangle properties, and anyone interested in understanding the relationships between angles and sides in triangles.

Dantes
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Given 2 angles of a triangle, how many triangles are possible? Explain why.

Seeing how a triangle is 180 degrees, and if they give you two angles, that automatically locks the 3rd one at a certain value that will equal 180 when added with the other 2 angles. So I get 1.

My other idea was that it was infinity since you can divide the triangle with the two given sides into infinite smaller pieces as you get smaller and smaller.

I also think I might be missing a big point which is taking into consideration the sides of the triangle.

Any help would be very appreciated.
 
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Given 2 angles you can automatically get the third angle. So the angles and shape are fixed. However you can double each side and get the same shape. You could also triple the size, or as you say shrink the size etc. So their are an infinite number of triangles of different size but the same shape. The formal name for triangle with two equal sides is " similar triangles". The only slightly tricky thing in this area that your teachers may be ruthless is that if that given two sides and an the non-included angle you can make actually make two triangles. People ignore the fact that if the non included angle is greater than 90 degrees
 

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