В треугольнике со сторонами: a = 107.7, b = 105.4, с = 85 высоты равны ha = 77.08, hb = 78.77, hc = 97.67
Ответ:
a=107.7
b=105.4
c=85
α°=67.9°
β°=65.1°
γ°=47°
S = 4151
ha=77.08
hb=78.77
hc=97.67
P = 298.1
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 67.9° - 65.1°
= 47°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 85·
sin(67.9°)
sin(47°)
= 85·
0.9265
0.7314
= 85·1.267
= 107.7
Сторона:
b = c·
sin(β°)
sin(γ°)
= 85·
sin(65.1°)
sin(47°)
= 85·
0.907
0.7314
= 85·1.24
= 105.4
Периметр:
P = a + b + c
= 107.7 + 105.4 + 85
= 298.1
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√149.05·(149.05-107.7)·(149.05-105.4)·(149.05-85)
=√149.05 · 41.35 · 43.65 · 64.05
=√17231015.630194
= 4151
Высота :
ha =
2S
a
=
2 · 4151
107.7
= 77.08
hb =
2S
b
=
2 · 4151
105.4
= 78.77
hc =
2S
c
=
2 · 4151
85
= 97.67