В треугольнике со сторонами: a = 29.91, b = 90.81, с = 94.18 высоты равны ha = 90.7, hb = 29.87, hc = 28.8
Ответ:
a=29.91
b=90.81
c=94.18
α°=18.49°
β°=74.31°
γ°=86.91°
S = 1356.4
ha=90.7
hb=29.87
hc=28.8
P = 214.9
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
90.812+94.182-29.912
2·90.81·94.18
)
= arccos(
8246.4561+8869.8724-894.6081
17105
)
= 18.49°
Периметр:
P = a + b + c
= 29.91 + 90.81 + 94.18
= 214.9
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√107.45·(107.45-29.91)·(107.45-90.81)·(107.45-94.18)
=√107.45 · 77.54 · 16.64 · 13.27
=√1839740.0438144
= 1356.4
Высота :
ha =
2S
a
=
2 · 1356.4
29.91
= 90.7
hb =
2S
b
=
2 · 1356.4
90.81
= 29.87
hc =
2S
c
=
2 · 1356.4
94.18
= 28.8
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
90.81
29.91
sin(18.49°))
= arcsin(3.036·0.3171)
= 74.31°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
94.18
29.91
sin(18.49°))
= arcsin(3.149·0.3171)
= 86.91°