KazzLabs

Pythagorean theorem in practice

Definitions of variables in the right triangle

Definition of Unity Distance variable D1

4. Calculation of the right triangle based on dimensions and desired angle α.

Enter minimum and maximum values of a and b in range from 1 to 9999, accuracy in range from 0,00001 to 0,9 and angle α in range from 10° to 80° and click "Submit" button.

Maximum 100000 calculations (on the server side) will be performed and only the first 5000 results will be displayed.
Click on column label to change sorting. Rows marked with color are Pythagorean triples.

a	b	c	α	90°	max Δα	max Δ90°	D1(max Δα)	D1(max Δ90°)
56	97	112	30.0000°	89.9947°	0.0044°	0.0192°	12 933	2 977
–	–	–	# = 1	–	–	–	–	–

Checked 9801 combinations

Description:

a, b, c: sides of the triangle

max Δ(a,b,c): desired accuracy of dimensions

α ±: desired value and accuracy of angle α

α: calculated value of angle α assuming exact dimensions

90°: calculated value of 90° angle assuming exact dimensions

max Δα: maximal error of angle α

max Δ90°: maximal error of 90° angle

D1(max Δα): unity distance at angle (max Δα)

D1(max Δ90°): unity distance at angle (max Δ90°), helps to better understand small angles size

Let's suppose we're looking for data for a right triangle with an angle α of 30°±0.1° and a side length range of 2-100 cm ± 0.01 cm. We get a single result: (56,97,112) with an angle error of 0.0044° and a right angle error of 0.0192°.

When we increase the length range to 200cm, the best triplet is (112,194,224) with an error of Δα=0.0022° and an error of Δ90°=0.0123°

These triples satisfy an approximate Pythagorean theorem, e.g. √(112²+194²)=224.0089≈224.

For an angle of 45° these will be, for example, the numbers (70,70,99) with errors of 0.0099° and 0.0198° or (169,169,239) with errors of 0.0034° and 0.0068°