Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √6.12 + 62 - 2·6.1·6·cos(20°)
= √37.21 + 36 - 73.2·0.9397
= √4.424
= 2.103
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(20°))
= arcsin(2.901·0.342)
= 82.81°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(20°))
= arcsin(2.853·0.342)
= 77.35°
Периметр:
P = a + b + c
= 2.103 + 6.1 + 6
= 14.2
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√7.102·(7.102-2.103)·(7.102-6.1)·(7.102-6)
=√7.102 · 4.999 · 1.002 · 1.102
=√39.202441983192
= 6.261
Высота :
ha =
=
= 5.954
hb =
=
= 2.053
hc =
=
= 2.087