Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5482 + 5002 - 2·548·500·cos(160°)
= √300304 + 250000 - 548000·-0.9397
= √1065260
= 1032.1
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(160°))
= arcsin(0.531·0.342)
= 10.46°
или:
α° = arccos(
)
= arccos(
5002+1032.12-5482
2·500·1032.1
)
= arccos(
250000+1065230.41-300304
1032100
)
= 10.47°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(160°))
= arcsin(0.4844·0.342)
= 9.536°
Периметр:
P = a + b + c
= 548 + 500 + 1032.1
= 2080.1
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√1040.1·(1040.1-548)·(1040.1-500)·(1040.1-1032.1)
=√1040.1 · 492.1 · 540.1 · 8
=√2211528933.768
= 47026.9
Высота :
ha =
=
= 171.63
hb =
=
= 188.11
hc =
=
= 91.13