Find Angles in Right Angle Triangles

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Discussion Overview

The discussion centers around the possibility of calculating angles in right-angle triangles when the lengths of all three sides are known, specifically without using trigonometric functions. The scope includes theoretical considerations and alternative methods of angle calculation.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether it is possible to calculate angles without using trigonometric functions if all three sides of a right-angle triangle are known.
  • Another participant suggests that side ratios correspond to trigonometric functions of the angles and mentions the possibility of approximating angles using power series of inverse trigonometric functions.
  • A third participant expresses confusion about the original question, arguing that trigonometric functions are specifically designed for this purpose and likens the inquiry to asking if one can find a sum without using addition.
  • Another participant notes that there are specific geometric cases (like 45/45 degrees or 30/60 degrees) where angles can be determined without trigonometric functions.
  • A fifth participant points out the etymology of 'trigonometry' as relating to the measurement of angles in triangles, reinforcing the idea that trigonometric functions are inherently linked to the problem at hand.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and validity of using trigonometric functions for angle calculation in right-angle triangles. Some argue for the inherent role of trigonometry, while others explore alternative methods or special cases.

Contextual Notes

The discussion does not resolve the question of whether angles can be calculated without trigonometric functions and highlights the dependence on definitions and interpretations of the problem.

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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