Undergrad Find Angles in Right Angle Triangles

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SUMMARY

Calculating angles in right-angle triangles using only the lengths of the three sides is fundamentally linked to trigonometric functions. The discussion highlights that while trigonometric functions are the standard method for determining angles, approximations can be made using power series of inverse trigonometric functions. Special cases, such as 45/45 degrees and 30/60 degrees triangles, can be solved using geometric principles. The etymology of 'trigonometry' emphasizes its purpose as a measurement of angles in triangles.

PREREQUISITES
  • Understanding of right-angle triangle properties
  • Familiarity with trigonometric functions
  • Knowledge of power series and their applications
  • Basic geometric principles related to triangles
NEXT STEPS
  • Research the power series of inverse trigonometric functions
  • Study the properties of special right triangles (30-60-90 and 45-45-90)
  • Explore geometric methods for angle calculation in triangles
  • Learn about the historical development of trigonometry and its applications
USEFUL FOR

Mathematicians, educators, students studying geometry and trigonometry, and anyone interested in alternative methods for calculating angles in triangles.

Sameh soliman
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TL;DR
If it we know 3 sides of a right angle triangle, will it be possible to calculate the angles without using trig. Functions
If it we know 3 sides of a right angle triangle, will it be possible to calculate the angles without using trig. Functions
 
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The side ratios are trig. functions of the angles. You can approximate angles using the power series of the inverse trig. functions.
 
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Sameh soliman said:
Summary:: If it we know 3 sides of a right angle triangle, will it be possible to calculate the angles without using trig. Functions

If it we know 3 sides of a right angle triangle, will it be possible to calculate the angles without using trig. Functions
I'm trying to understand the reason for your question. This is what trig functions do. Why do you want another way to calculate the angles? What's wrong with trig functions? It's kind of like asking "can I find the sum of two numbers without using addition?"
 
That's exactly what trigonometric functions do.
There are some special cases where you can use geometry to find the angles, e.g. 45/45 degrees or 30/60 degrees.
 
Perhaps look at the etymology of 'trigonometry' ##-## 'tri - gono - metry' ##\leftrightarrow## 'three angle measurement' (or triangle measurement) ##-## exactly what you're seeking.
 

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