Question

Fie dreptunghiul ABCD cu AB=32 cm, BC=24 cm. Calculati:
a) lungimea diagonalei BD.
b) tg unghiului ACB
c) aria triunghiului AEC stiind ca AE perpendicular pe DB. (AE_|_DB)
Dau coroana

Answer 1

a) In ΔADB (dr.A) TP⇒ DB²=AD²+AB²=24²+32²=576+1024=1600 BD=√1600 BD=40 cm                       
b) in ΔACB (dr.B) ⇒ tg ACB = AB/BC=32/24=4/3   
c) AE=AD×AB/BD=24×32/40=96/5 cm  
AO = AC/2 = 40/2 = 20 cm          
In ΔAEO (dr.E) TP⇒ EO²=AO²-AE²= 20²-(96/5)² = 400 - 9216/25 = (10000-9216)/25 = 784/25   EO=√)784/25)= 28/5 cm  
Aria ΔAEC = 2×Aria ΔAEO = 2×AE×EO/2 = 96/5 × 28/5 = 2688/25 cm