Решение:
Угол:
α° = arccos(
)
= arccos(
57002+191002-223002
2·5700·19100
)
= arccos(
32490000+364810000-497290000
217740000
)
= 117.34°
Периметр:
P = a + b + c
= 22300 + 5700 + 19100
= 47100
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√23550·(23550-22300)·(23550-5700)·(23550-19100)
=√23550 · 1250 · 17850 · 4450
=√2.33829421875E+15
= 48355912
Высота :
ha =
=
= 4336.9
hb =
=
= 16967
hc =
=
= 5063.4
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(117.34°))
= arcsin(0.2556·0.8883)
= 13.12°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(117.34°))
= arcsin(0.8565·0.8883)
= 49.54°