Question

1. in triunghiul abc, m a =90,m B = 30, ac =8 cm, ab =6 cm ,ad|bc d€bc, calculati lungimea inaltimii corespunzatoare ipotenuzei cos C, sin B,tg C
2.in triunghiu abc, m a =90 , AD | BC , D € BC, Dc= 54 cm, bc= 60 cm
calculati lungimile segmentelor bd ad, sin C, cos b, tg C,ctg b

Answer 1

Răspuns:

Explicație pas cu pas:

∡A=90°   ∡B=30°   AC=8 cm   AB=6 cm

T Pitagora

BC²=AB²+AC²=36+64=100      ⇒BC=10 cm

daca ∡B=30° ⇒ AD=AB/2     AD=6/2==3 cm

cosC=sin B=1/2      ∡C=60°

sin B=sin 30°=1/2

tg C=sinC/cosC=√3

2

DC=54 cm  BC=60 cm

BD=BC-DC=60-54=6cm

AD²=BD×DC=54×6=6×9×6              AD=6×3=18 cm

AC²=DC×BC=54×60=6×9×6×10         AC=18√10 cm

sinC=AD/AC=18/18√10=√10/10

cosB=sinC=√10/10

tgC=AD/DC=18/54=1/3

ctg B=tgC=1/3