В треугольнике со сторонами: a = 2, b = 2.0, с = 2.0 высоты равны ha = 1.7, hb = 1.732, hc = 1.732
Ответ:
a=2
b=2.0
c=2.0
α°=60°
β°=60°
γ°=60°
S = 1.732
ha=1.7
hb=1.732
hc=1.732
P = 6
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
2.0
2.0
sin(60°))
= arcsin(1·0.866)
= 60°
Угол:
α° = 180 - γ° - β°
= 180 - 60° - 60°
= 60°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √2.02 + 2.02 - 2·2.0·2.0·cos(60°)
= √4 + 4 - 8·0.5
= √4
= 2
или:
a = b·
sin(α°)
sin(β°)
= 2.0·
sin(60°)
sin(60°)
= 2.0·
0.866
0.866
= 2.0·1
= 2
или:
a = c·
sin(α°)
sin(γ°)
= 2.0·
sin(60°)
sin(60°)
= 2.0·
0.866
0.866
= 2.0·1
= 2
Периметр:
P = a + b + c
= 2 + 2.0 + 2.0
= 6
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3·(3-2)·(3-2.0)·(3-2.0)
=√3 · 1 · 1 · 1
=√3
= 1.732
hb =
2S
b
=
2 · 1.732
2.0
= 1.732
hc =
2S
c
=
2 · 1.732
2.0
= 1.732