Решение:
Угол:
α° = arccos(
)
= arccos(
1482.622+1373.062-1167.112
2·1482.62·1373.06
)
= arccos(
2198162.0644+1885293.7636-1362145.7521
4071452
)
= 48.06°
Периметр:
P = a + b + c
= 1167.11 + 1482.62 + 1373.06
= 4022.8
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√2011.4·(2011.4-1167.11)·(2011.4-1482.62)·(2011.4-1373.06)
=√2011.4 · 844.29 · 528.78 · 638.34
=√573214504252.87
= 757109.3
Высота :
ha =
=
= 1297.4
hb =
=
= 1021.3
hc =
=
= 1102.8
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(48.06°))
= arcsin(1.27·0.7438)
= 70.84°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(48.06°))
= arcsin(1.176·0.7438)
= 61.01°