Question

1. in dreptunghiul abcd ab=10 cm si ctg cbo = 1/2aflati sin bao
2. in rombul abcd dc=10 cm si tg bac=3/4 aflati ac si bd
3. Calculati aria triunghiului abc ac=20 cm bc=15 cm iar sin c=0,8
4. abc este treiunghi dreptunghic in a si sinusul unghiului b este 9/41 calculati cosinusul unghiului b si tg lui c

Answer 1

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Answer 2

1) ctg CBO=CB/CD
CD=AB=10cm.
1/2=CB/10⇒CB=10/2=5cm.
sin BAO=BC/AO.
ΔABC: AB²+BC²=AC²⇒AC²=10²+5²=5²(2²+1)=5²ori5.⇒AC=5√5cm.
AO=AC/2=5√5/2 cm
sin BAO=5/(5√5/2)=5ori2/5√5=2/√5=2√5/5

2) tg BAC=BO/AO⇒BO=3AO/4
ΔAOB: AO²+OB²=AB²
AB=CD=10cm
AO²+9AO²/4=100⇒13AO²=400⇒AO²=400/13⇒AO=20/√13=20√13/13cm.
AO=AC/2⇒AC=2AO=40√13/13 cm. BO=3AO/4=60√13/(4ori13)=15√13/13 cm.
BO=BD/2⇒BD=2BO=30√13/13 cm.

3) Aria triunghiului = (ACoriBCori sinC)/2=(20 ori 15 ori 0,8)/2= 240/2=120 cm²

4)  sin B=AC/BC
cos B=1/sin B=1/(9/41)=41/9
sin C=cos B=41/9
cos C=sin B=9/41
tg C=sinC/cosC=41/9/(9/41)=41ori41/81=1681/81