Решение:
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(45°))
= arcsin(1.414·0.7071)
= 88.97°
Высота :
hc = a·sin(β°)
= 700·sin(45°)
= 700·0.7071
= 494.97
Угол:
γ° = 180 - α° - β°
= 180 - 88.97° - 45°
= 46.03°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √7002 + 4952 - 2·700·495·cos(46.03°)
= √490000 + 245025 - 693000·0.6943
= √253875.1
= 503.86
или:
c = a·
= 700·
= 700·
= 700·0.7198
= 503.86
или:
c = b·
= 495·
= 495·
= 495·1.018
= 503.91
Периметр:
P = a + b + c
= 700 + 495 + 503.91
= 1698.9
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√849.46·(849.46-700)·(849.46-495)·(849.46-503.91)
=√849.46 · 149.46 · 354.46 · 345.55
=√15550560301.113
= 124701.9
Высота :
ha =
=
= 356.29
hb =
=
= 503.85