В треугольнике со сторонами: a = 5.627, b = 6.115, с = 9 высоты равны ha = 6.017, hb = 5.537, hc = 3.762
Ответ:
a=5.627
b=6.115
c=9
α°=38°
β°=42°
γ°=100°
S = 16.93
ha=6.017
hb=5.537
hc=3.762
P = 20.74
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 38° - 42°
= 100°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 9·
sin(38°)
sin(100°)
= 9·
0.6157
0.9848
= 9·0.6252
= 5.627
Сторона:
b = c·
sin(β°)
sin(γ°)
= 9·
sin(42°)
sin(100°)
= 9·
0.6691
0.9848
= 9·0.6794
= 6.115
Периметр:
P = a + b + c
= 5.627 + 6.115 + 9
= 20.74
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.37·(10.37-5.627)·(10.37-6.115)·(10.37-9)
=√10.37 · 4.743 · 4.255 · 1.37
=√286.7160551085
= 16.93
Высота :
ha =
2S
a
=
2 · 16.93
5.627
= 6.017
hb =
2S
b
=
2 · 16.93
6.115
= 5.537
hc =
2S
c
=
2 · 16.93
9
= 3.762