If I know the length of all 3 sides in a right angle triangle, how do I get the degrees of the other angles? Which formula do I use again?
tan α = opposite cathetus/adjacent cathetus
Given the three sides (the largest must be less than the sum of the other two)
Find any angle from cosA = (b^2 + c^2 - a^2)/2bc.
The remaining angles can be derived from the Law of Sines.
Alternatively, find any angle, A for instance, using tan(A/2) = r/(s - a) where s = (a + b + c)/2 and r = sqrt[(s - a)(s - b)(s - c)/s] (the radius of the inscribed circle). The remaining angles can be derived using the same expression or from the Law of Sines.
Alternatively, one angle can be derived from sin(A/2) = sqrt[(s - b)(s - c)/bc] or cos(A/2) = sqrt[s(s - a)/bc].
To find the degrees of the other angles in a right-angled triangle when you know the lengths of all three sides, you can use the trigonometric ratios. Specifically, you would use the inverse trigonometric functions, such as arcsine, arccosine, or arctangent.
In a right-angled triangle, one angle is always 90 degrees. Let's call this angle A. The other two angles are B and C.
To find angle B, you can use the inverse sine function (arcsine). The formula is:
B = arcsin(opposite / hypotenuse)
To find angle C, you can use the inverse cosine function (arccosine). The formula is:
C = arccos(adjacent / hypotenuse)
Alternatively, if you know the lengths of the sides opposite and adjacent to angle B or C, you can use the inverse tangent function (arctangent). The formula is:
B = arctan(opposite / adjacent)
C = arctan(adjacent / opposite)
Note that when using these formulas, make sure to use the sides corresponding to the angles B and C.
Remember to convert the angles from radians to degrees if necessary.