В треугольнике со сторонами: a = 1.732, b = 2, с = 1 высоты равны ha = 1, hb = 0.866, hc = 1.732
Ответ:
a=1.732
b=2
c=1
α°=60°
β°=90°
γ°=30°
S = 0.866
ha=1
hb=0.866
hc=1.732
P = 4.732
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 60° - 90°
= 30°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 1·
sin(60°)
sin(30°)
= 1·
0.866
0.5
= 1·1.732
= 1.732
Сторона:
b = c·
sin(β°)
sin(γ°)
= 1·
sin(90°)
sin(30°)
= 1·
1
0.5
= 1·2
= 2
Периметр:
P = a + b + c
= 1.732 + 2 + 1
= 4.732
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√2.366·(2.366-1.732)·(2.366-2)·(2.366-1)
=√2.366 · 0.634 · 0.366 · 1.366
=√0.749955998064
= 0.866
Высота :
ha =
2S
a
=
2 · 0.866
1.732
= 1
hb =
2S
b
=
2 · 0.866
2
= 0.866
hc =
2S
c
=
2 · 0.866
1
= 1.732