Question Number 134637 by bobhans last updated on 06/Mar/21
$$\mathcal{G}\mathrm{eometry} \\ $$How can you compute the length of the sides of a triangle given the area and three angles in the law of Tangent?
Answered by benjo_mathlover last updated on 06/Mar/21
$$\mathrm{Height}\:=\:\mathrm{h}\:=\sqrt{\frac{\mathrm{2tan}\:\beta.\mathrm{Area}}{\mathrm{tan}\:\alpha\left(\mathrm{tan}\:\alpha+\mathrm{tan}\:\beta\right)}} \\ $$$$\mathrm{Base}\:=\:\mathrm{b}\:=\:\mathrm{h}.\mathrm{tan}\:\alpha\left(\frac{\mathrm{tan}\:\beta+\mathrm{tan}\:\alpha}{\mathrm{tan}\:\beta}\right) \\ $$$$\mathrm{The}\:\mathrm{side}\:\mathrm{above}\:\alpha\:=\:\frac{\mathrm{h}}{\mathrm{sin}\:\alpha} \\ $$$$\mathrm{The}\:\mathrm{side}\:\mathrm{above}\:\beta\:=\:\frac{\mathrm{h}}{\mathrm{sin}\:\beta}\: \\ $$
Commented by benjo_mathlover last updated on 06/Mar/21
