Решение:
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(60°))
= arcsin(0.6667·0.866)
= 35.27°
Высота :
hc = a·sin(β°)
= 20·sin(60°)
= 20·0.866
= 17.32
Угол:
γ° = 180 - α° - β°
= 180 - 35.27° - 60°
= 84.73°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √202 + 302 - 2·20·30·cos(84.73°)
= √400 + 900 - 1200·0.09185
= √1189.8
= 34.49
или:
c = a·
= 20·
= 20·
= 20·1.725
= 34.5
или:
c = b·
= 30·
= 30·
= 30·1.15
= 34.5
Периметр:
P = a + b + c
= 20 + 30 + 34.5
= 84.5
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√42.25·(42.25-20)·(42.25-30)·(42.25-34.5)
=√42.25 · 22.25 · 12.25 · 7.75
=√89247.18359375
= 298.74
Высота :
ha =
=
= 29.87
hb =
=
= 19.92