Question Number 151189 by mathdanisur last updated on 18/Aug/21
$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}:\:\left(\boldsymbol{\varphi}-\mathrm{golden}\:\mathrm{ratio}\right) \\ $$$$\mathrm{sinA}\:+\:\frac{\mathrm{sinB}}{\boldsymbol{\varphi}}\:+\:\frac{\mathrm{sinC}}{\boldsymbol{\varphi}}\:<\:\frac{\mathrm{1}}{\boldsymbol{\varphi}}\:+\:\frac{\mathrm{1}+\sqrt{\boldsymbol{\varphi}}+\boldsymbol{\varphi}}{\mathrm{2}\boldsymbol{\varphi}} \\ $$