В треугольнике со сторонами: a = 2716.9, b = 2675.8, с = 95.7 высоты равны ha = 85.76, hb = 87.08, hc = 2434.6
Ответ:
a=2716.9
b=2675.8
c=95.7
α°=114.96°
β°=63.21°
γ°=1.83°
S = 116497.7
ha=85.76
hb=87.08
hc=2434.6
P = 5488.4
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 114.96° - 63.21°
= 1.83°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 95.7·
sin(114.96°)
sin(1.83°)
= 95.7·
0.9066
0.03193
= 95.7·28.39
= 2716.9
Сторона:
b = c·
sin(β°)
sin(γ°)
= 95.7·
sin(63.21°)
sin(1.83°)
= 95.7·
0.8927
0.03193
= 95.7·27.96
= 2675.8
Периметр:
P = a + b + c
= 2716.9 + 2675.8 + 95.7
= 5488.4
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√2744.2·(2744.2-2716.9)·(2744.2-2675.8)·(2744.2-95.7)
=√2744.2 · 27.3 · 68.4 · 2648.5
=√13571707342.284
= 116497.7
Высота :
ha =
2S
a
=
2 · 116497.7
2716.9
= 85.76
hb =
2S
b
=
2 · 116497.7
2675.8
= 87.08
hc =
2S
c
=
2 · 116497.7
95.7
= 2434.6