Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √1002 + 4402 - 2·100·440·cos(90°)
= √10000 + 193600 - 88000·0
= √203600
= 451.22
Высота :
hc = a·sin(β°)
= 100·sin(90°)
= 100·1
= 100
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(90°))
= arcsin(0.2216·1)
= 12.8°
или:
α° = arccos(
)
= arccos(
451.222+4402-1002
2·451.22·440
)
= arccos(
203599.4884+193600-10000
397073.6
)
= 12.8°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(90°))
= arcsin(0.9751·1)
= 77.19°
Периметр:
P = a + b + c
= 100 + 451.22 + 440
= 991.22
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√495.61·(495.61-100)·(495.61-451.22)·(495.61-440)
=√495.61 · 395.61 · 44.39 · 55.61
=√483999999.98364
= 22000
Высота :
ha =
=
= 440
hb =
=
= 97.51