Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √2002 + 2002 - 2·200·200·cos(100°)
= √40000 + 40000 - 80000·-0.1736
= √93888
= 306.41
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(100°))
= arcsin(0.6527·0.9848)
= 40°
или:
α° = arccos(
)
= arccos(
2002+306.412-2002
2·200·306.41
)
= arccos(
40000+93887.0881-40000
122564
)
= 40°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(100°))
= arcsin(0.6527·0.9848)
= 40°
Периметр:
P = a + b + c
= 200 + 200 + 306.41
= 706.41
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√353.21·(353.21-200)·(353.21-200)·(353.21-306.41)
=√353.21 · 153.21 · 153.21 · 46.8
=√388019068.68633
= 19698.2
Высота :
ha =
=
= 196.98
hb =
=
= 196.98
hc =
=
= 128.57