Решение:
Угол:
α° = arccos(
)
= arccos(
138002+117002-210002
2·13800·11700
)
= arccos(
190440000+136890000-441000000
322920000
)
= 110.61°
Периметр:
P = a + b + c
= 21000 + 13800 + 11700
= 46500
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√23250·(23250-21000)·(23250-13800)·(23250-11700)
=√23250 · 2250 · 9450 · 11550
=√5.70977859375E+15
= 75563077
Высота :
ha =
=
= 7196.5
hb =
=
= 10951.2
hc =
=
= 12916.8
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(110.61°))
= arcsin(0.6571·0.936)
= 37.96°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(110.61°))
= arcsin(0.5571·0.936)
= 31.43°