Undergrad Find Angles in Right Angle Triangles

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Calculating angles in a right triangle using only the lengths of the sides is fundamentally tied to trigonometric functions, which are designed for this purpose. While there are special cases where geometry can provide angle measures, such as in 45/45 or 30/60 triangles, these are exceptions rather than general solutions. The discussion emphasizes that seeking alternative methods to find angles without trigonometry is akin to asking for a way to perform addition without using the addition operation. Understanding the role of trigonometric functions is essential for solving such problems effectively. Ultimately, trigonometry remains the most reliable method for angle calculation in right triangles.
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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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