Question

Buna ma puteti ajuta la un exercitiu?
1. Se considera triunghiul dreptunghic ABC, m( a) Daca AB=16cm, BC=20cm, calculati: AC, sin C, cos C, tg B, ctg B
b) Daca BC=40cm si sin C= 4supra5, calculati: AB, AC, sin B, cos B,cos C, tg C, ctg C
c)Daca AB=12cm si cos B=1supra2, calculati: BC, AC, sin C, cos C, sin B, tg B,tg C, ctg C
d) Daca AC=12cm si tg C=1,25, calculati: AB, BC, sin B, cos B. Va rog ajutati-ma ca o sa imi puna nota pe tema asta!!

Answer 1

a. AC=√(20²-16²)=√(400-256)=√144=12 cm
sin C=AB/BC=16/20=4/5
cos C=AC/BC=12/20=3/5
tg B =AC/AB=12/16=3/4
ctg B =AB/AC=16/12=4/3

b.sin C=AB/BC=AB/40=4/5  ⇒ AB=32 cm
AC=√(40²-32²)=√(1600-1024)=√576=24 cm
sin B=AC/BC=24/40=3/5
cos B=AB/BC=32/40=4/5
cos C=AC/BC=24/40=3/5
tg C =AB/AC=32/24=4/3
ctg C =AC/AB=24/32=3/4

c.cos B =AB/BC=12/BC=1/2  ⇒ BC=24 cm
AC=√(24²-12²)=√(576-144)=√432=12√3 cm
sin C=AB/BC=12/24=1/2
cos C=AC/BC=12√3/24=√3/2
tg B =AC/AB=12√3/12=√3
tg C =AB/AC=12/12√3=1/√3=√3/3
ctg C =AC/AB=12√3/12=√3

d.tg C =AB/AC=AB/12=1,25  ⇒ AB=15 cm
BC=√(15²+12²)=√(225+144)=√369=3√41 cm
sin B=AC/BC=12/3√41=4/√41
cos B=AB/BC=15/3√41=5/√41