Решение:
Угол:
α° = arccos(
)
= arccos(
133002+96002-167002
2·13300·9600
)
= arccos(
176890000+92160000-278890000
255360000
)
= 92.21°
Периметр:
P = a + b + c
= 16700 + 13300 + 9600
= 39600
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√19800·(19800-16700)·(19800-13300)·(19800-9600)
=√19800 · 3100 · 6500 · 10200
=√4.069494E+15
= 63792586
Высота :
ha =
=
= 7639.8
hb =
=
= 9592.9
hc =
=
= 13290.1
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(92.21°))
= arcsin(0.7964·0.9993)
= 52.73°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(92.21°))
= arcsin(0.5749·0.9993)
= 35.06°