Question

calcularea lungimea laturilor GE si GF unui triunghi dreptunghic daca tgE=0.6 si EF=3

Answer 1

Varianta 1
ΔEFG dreptunghic si ∡EGF=90°
tg E=EG/EF⇒ EG/FG=6/10=3/5⇒ FG=5EG/3
EF² = FG²+EG² ⇒ 3² = (5EG/3)² + EG²
9= 25EG²/9+EG² ⇒ 9 = (25EG² +9EG²) :9
81= 34 EG² ⇒ EG=√81/√34= 9√34/34
FG= 45√34/102=15√34/34

Varianta 2
ΔEGF dreptunghic si ∡GFE=90°
tg E= GF/EF⇒ GF/EF=6/10=3/5
⇒ 5GF=3EF⇒ 5GF=9⇒ GF=9/5
EG² = GF² +FE² ⇒ EG²= 81/25+ 225/25= 306/25
⇒EG= 3√34/5