Решение:
Угол:
α° = arccos(
)
= arccos(
120002+55002-120002
2·12000·5500
)
= arccos(
144000000+30250000-144000000
132000000
)
= 76.75°
Периметр:
P = a + b + c
= 12000 + 12000 + 5500
= 29500
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√14750·(14750-12000)·(14750-12000)·(14750-5500)
=√14750 · 2750 · 2750 · 9250
=√1.03180859375E+15
= 32121778
Высота :
ha =
=
= 5353.6
hb =
=
= 5353.6
hc =
=
= 11680.6
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(76.75°))
= arcsin(1·0.9734)
= 76.76°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(76.75°))
= arcsin(0.4583·0.9734)
= 26.49°