Решение:
Угол:
α° = arccos(
)
= arccos(
95002+55002-137002
2·9500·5500
)
= arccos(
90250000+30250000-187690000
104500000
)
= 130.01°
Периметр:
P = a + b + c
= 13700 + 9500 + 5500
= 28700
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√14350·(14350-13700)·(14350-9500)·(14350-5500)
=√14350 · 650 · 4850 · 8850
=√4.0035961875E+14
= 20008988
Высота :
ha =
=
= 2921
hb =
=
= 4212.4
hc =
=
= 7276
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(130.01°))
= arcsin(0.6934·0.7659)
= 32.08°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(130.01°))
= arcsin(0.4015·0.7659)
= 17.91°