Решение:
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(65°))
= arcsin(1·0.9063)
= 65°
Угол:
α° = 180 - γ° - β°
= 180 - 65° - 65°
= 50°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √2.02 + 2.02 - 2·2.0·2.0·cos(50°)
= √4 + 4 - 8·0.6428
= √2.858
= 1.691
или:
a = b·
= 2.0·
= 2.0·
= 2.0·0.8452
= 1.69
или:
a = c·
= 2.0·
= 2.0·
= 2.0·0.8452
= 1.69
Периметр:
P = a + b + c
= 1.69 + 2.0 + 2.0
= 5.69
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√2.845·(2.845-1.69)·(2.845-2.0)·(2.845-2.0)
=√2.845 · 1.155 · 0.845 · 0.845
=√2.346268299375
= 1.532
hb =
=
= 1.532
hc =
=
= 1.532