Question

38. Aflaţi măsurile unghiurilor unui triunghi ABC,
știind că:
sunt direct proportionale cu numerele 7, 11 şi
12:
b) sunt invers proportionale cu numerele 0,2; 0.(3)
şi 1:
ajutor va rog!!!

Answer 1

Răspuns:

a) ∡A+∡B+∡C=180°

{∡A,∡B,∡C}d.p(direct proportionale)→{7,11,12}⇒

∡A/7=∡B/11=∡C/12=K

∡A/7=K/1⇒

∡A=7K

∡B/11=K/1⇒∡B=11K

∡C/12=K/1⇒∡C=12K

7K+11K+12K=30K=180°

30K=180°⇒K=180/30⇒K=6°

∡A=7K=7×6=42°

∡B=11K=11×6=66°

∡C=12K=12×6=72°

b){∡A,∡B,∡C}→I.P( INVERS PROPORTIONALE){0,2;0,(3);1}

0,2=2/10=1/5

0,(3)=3/9=1/3

1=1/1

∡A×1/5=∡B×1/3=∡C×1/1=K

∡A×1/5=K⇒A=K:1/5=K×5/1=5K

∡B×1/3=K⇒B=K:1/3=K×1/3=3K

∡C×1/1=K⇒C=K:1/1=K

5K+3K+K=180°

9K=180°

K=20°

∡A=5K=5×20=100°

∡B=3K=3×20=60°

∡C=K=20°