Решение:
Сторона:
b = c·
= 1.6·
= 1.6·
= 1.6·1.393
= 2.229
Угол:
α° = 180 - γ° - β°
= 180 - 45° - 80°
= 55°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √2.2292 + 1.62 - 2·2.229·1.6·cos(55°)
= √4.968 + 2.56 - 7.133·0.5736
= √3.437
= 1.854
или:
a = b·
= 2.229·
= 2.229·
= 2.229·0.8318
= 1.854
или:
a = c·
= 1.6·
= 1.6·
= 1.6·1.159
= 1.854
Периметр:
P = a + b + c
= 1.854 + 2.229 + 1.6
= 5.683
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√2.842·(2.842-1.854)·(2.842-2.229)·(2.842-1.6)
=√2.842 · 0.988 · 0.613 · 1.242
=√2.137780388016
= 1.462
hb =
=
= 1.312
hc =
=
= 1.828