Решение:
Угол:
α° = arccos(
)
= 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 =
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 =
=
= 90.7
hb =
=
= 29.87
hc =
=
= 28.8
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(18.49°))
= arcsin(3.036·0.3171)
= 74.31°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(18.49°))
= arcsin(3.149·0.3171)
= 86.91°