Question

Fie triungiul ABC cu m(BAC)=90° masura ungiului ABC=60° ADperpendicularpeBC,d apartine bc.
M-mijlBC
Am =8
Afla Ad si aria triungiulii abc

Answer 1

daca m mijlocul lui bc iar Δabc este dreptunghic (∡a=90°)=> m este mediana => am=bc/2
     8=bc/2=>bc=2×8=>bc=16
daca ∡a=90° si ∡b=60°=>∡c=30°
teorema unghului de 30°=> ab=bc/2=>ab=16/2=>ab=8
teorema catetei
ab²=bc×bd
8²=16×bd
64=16×bd=>bd=64/16=>bd=4
daca bc=16=>dc=bc-db=>cd=16-4=>cd=12
teorema inaltimii
ad²=bd×cd
ad²=4×12
ad²=48=>ad=√48=>ad=2√12
ariaΔ abc=bc×ad/2=16×2√12/2=16√12