Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √2002 + 2002 - 2·200·200·cos(179°)
= √40000 + 40000 - 80000·-0.9998
= √159984
= 399.98
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(179°))
= arcsin(0.5·0.01745)
= 0.4999°
или:
α° = arccos(
)
= arccos(
2002+399.982-2002
2·200·399.98
)
= arccos(
40000+159984.0004-40000
159992
)
= 0.573°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(179°))
= arcsin(0.5·0.01745)
= 0.4999°
Периметр:
P = a + b + c
= 200 + 200 + 399.98
= 799.98
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√399.99·(399.99-200)·(399.99-200)·(399.99-399.98)
=√399.99 · 199.99 · 199.99 · 0.0099999999999909
=√159980.00079984
= 399.98
Высота :
ha =
=
= 4
hb =
=
= 4
hc =
=
= 2