Решение:
Угол:
α° = arccos(
)
= arccos(
)
= arccos(
469225+400689-617796
867210
)
= 73.1°
Периметр:
P = a + b + c
= 786 + 685 + 633
= 2104
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√1052·(1052-786)·(1052-685)·(1052-633)
=√1052 · 266 · 367 · 419
=√43030606136
= 207438.2
Высота :
ha =
=
= 527.83
hb =
=
= 605.66
hc =
=
= 655.41
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(73.1°))
= arcsin(0.8715·0.9568)
= 56.5°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(73.1°))
= arcsin(0.8053·0.9568)
= 50.4°