В треугольнике со сторонами: a = 1122.2, b = 1072.2, с = 94.3 высоты равны ha = 78.22, hb = 81.87, hc = 930.83
Ответ:
a=1122.2
b=1072.2
c=94.3
α°=120.04°
β°=55.79°
γ°=4.17°
S = 43888.4
ha=78.22
hb=81.87
hc=930.83
P = 2288.7
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 120.04° - 55.79°
= 4.17°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 94.3·
sin(120.04°)
sin(4.17°)
= 94.3·
0.8657
0.07272
= 94.3·11.9
= 1122.2
Сторона:
b = c·
sin(β°)
sin(γ°)
= 94.3·
sin(55.79°)
sin(4.17°)
= 94.3·
0.827
0.07272
= 94.3·11.37
= 1072.2
Периметр:
P = a + b + c
= 1122.2 + 1072.2 + 94.3
= 2288.7
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√1144.4·(1144.4-1122.2)·(1144.4-1072.2)·(1144.4-94.3)
=√1144.4 · 22.2 · 72.2 · 1050.1
=√1926188029.8096
= 43888.4
Высота :
ha =
2S
a
=
2 · 43888.4
1122.2
= 78.22
hb =
2S
b
=
2 · 43888.4
1072.2
= 81.87
hc =
2S
c
=
2 · 43888.4
94.3
= 930.83