Question

1.Calculati aria si inaltimea unui triunghi dreptunghic cu o cateta de 12cm si un unghi de 45 grade ​

Answer 1

Fie ΔABC-dreptunghic, cu ∡A=90°; ∡B=45°

∡A=90°(1)

∡B=45°(2)

AB=12cm9=(3)

din (1),(2),(3)⇒ΔABC-isoscel dreptunghic

⇒∡B=∡C=45°

AB=AC=12cm

A=c₁·c₂ /2 = 12·12/2= 12·6=72cm²

ΔABC dreptunghic⇒(TP) BC²=AB²+AC²

⇒BC²=12²+12²=144+144=288 cm

⇒BC=√288cm =12√2 cm

h=c₁·c₂/ip= AB·AC/BC=12·12/12√2=6√2cm

----→ΔTriunghiul1Δ←----

Answer 2

Răspuns:

∡B = 45° => triunghi isoscel => AB = AC = 12cm

A = AB×AC/2 = 144cm²/2 = 72 cm²

BC = 2√AB = 12√2 cm

AB×AC = AD×BC =>

AD = AB×AC/BC

= 144cm²/12√2 cm

= 12/√2 cm

= 12√2/2 cm

= 6√2 cm