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?
2 answers
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].
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].
2 answers