В треугольнике со сторонами: a = -796.53, b = -836.22, с = 86.27 высоты равны ha = -78.4, hb = -74.68, hc = 723.83
Ответ:
a=-796.53
b=-836.22
c=86.27
α°=120.04°
β°=65.34°
γ°=-5.38°
S = 31222.6
ha=-78.4
hb=-74.68
hc=723.83
P = -1546.5
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 120.04° - 65.34°
= -5.38°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 86.27·
sin(120.04°)
sin(-5.38°)
= 86.27·
0.8657
-0.09376
= 86.27·-9.233
= -796.53
Сторона:
b = c·
sin(β°)
sin(γ°)
= 86.27·
sin(65.34°)
sin(-5.38°)
= 86.27·
0.9088
-0.09376
= 86.27·-9.693
= -836.22
Периметр:
P = a + b + c
= -796.53 + -836.22 + 86.27
= -1546.5
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√-773.24·(-773.24--796.53)·(-773.24--836.22)·(-773.24-86.27)
=√-773.24 · 23.29 · 62.98 · -859.51
=√974849090.53987
= 31222.6
Высота :
ha =
2S
a
=
2 · 31222.6
-796.53
= -78.4
hb =
2S
b
=
2 · 31222.6
-836.22
= -74.68
hc =
2S
c
=
2 · 31222.6
86.27
= 723.83