Решение:
Угол:
α° = arccos(
)
= arccos(
65002+99002-143002
2·6500·9900
)
= arccos(
42250000+98010000-204490000
128700000
)
= 119.94°
Периметр:
P = a + b + c
= 14300 + 6500 + 9900
= 30700
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√15350·(15350-14300)·(15350-6500)·(15350-9900)
=√15350 · 1050 · 8850 · 5450
=√7.7738731875E+14
= 27881666
Высота :
ha =
=
= 3899.5
hb =
=
= 8579
hc =
=
= 5632.7
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(119.94°))
= arcsin(0.4545·0.8665)
= 23.19°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(119.94°))
= arcsin(0.6923·0.8665)
= 36.86°