Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √1662 + 7672 - 2·166·767·cos(178.71°)
= √27556 + 588289 - 254644·-0.9997
= √870412.6
= 932.96
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(178.71°))
= arcsin(0.1779·0.02251)
= 0.2294°
или:
α° = arccos(
)
= arccos(
7672+932.962-1662
2·767·932.96
)
= arccos(
588289+870414.3616-27556
1431161
)
= 0.2501°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(178.71°))
= arcsin(0.8221·0.02251)
= 1.06°
Периметр:
P = a + b + c
= 166 + 767 + 932.96
= 1866
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√932.98·(932.98-166)·(932.98-767)·(932.98-932.96)
=√932.98 · 766.98 · 165.98 · 0.019999999999982
=√2375429.4105257
= 1541.2
Высота :
ha =
=
= 18.57
hb =
=
= 4.019
hc =
=
= 3.304