Решение:
Угол:
α° = arccos(
)
= arccos(
82002+88002-110002
2·8200·8800
)
= arccos(
67240000+77440000-121000000
144320000
)
= 80.56°
Периметр:
P = a + b + c
= 11000 + 8200 + 8800
= 28000
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√14000·(14000-11000)·(14000-8200)·(14000-8800)
=√14000 · 3000 · 5800 · 5200
=√1.26672E+15
= 35591010
Высота :
ha =
=
= 6471.1
hb =
=
= 8680.7
hc =
=
= 8088.9
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(80.56°))
= arcsin(0.7455·0.9865)
= 47.34°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(80.56°))
= arcsin(0.8·0.9865)
= 52.11°