Решение:
Угол:
α° = arccos(
)
= arccos(
120002+96002-213002
2·12000·9600
)
= arccos(
144000000+92160000-453690000
230400000
)
= 160.76°
Периметр:
P = a + b + c
= 21300 + 12000 + 9600
= 42900
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√21450·(21450-21300)·(21450-12000)·(21450-9600)
=√21450 · 150 · 9450 · 11850
=√3.6030369375E+14
= 18981667
Высота :
ha =
=
= 1782.3
hb =
=
= 3163.6
hc =
=
= 3954.5
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(160.76°))
= arcsin(0.5634·0.3295)
= 10.7°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(160.76°))
= arcsin(0.4507·0.3295)
= 8.54°