Question

triunghiul ABC este dreptunghic in A si D=pr bc A. Daca AD=8cm si BD=4 cm , calculati sin B + sin C

Answer 1

[tex]\Delta ABD, \; m(\widehat{BDA})=90 : AB=\sqrt{AD^2+BD^2}=4\sqrt5\\ t. inaltimii\Rightarrow AD^2=BD\cdot DC \Rightarrow DC=\dfrac{AD^2}{BD}=16\\ BC=BD+DC=4+16=20\\ Pitagora \Rightarrow AC=\sqrt{BC^2-AB^2}=8\sqrt5\\ \sin B=\dfrac{AC}{BC}=\dfrac{2\sqrt5}{5}\\ \sin C=\dfrac{AB}{BC}=\dfrac{\sqrt5}{5}\\ \sin B + \sin C = \dfrac{3\sqrt5}{5}[/tex]