Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √142 + 102 - 2·14·10·cos(60°)
= √196 + 100 - 280·0.5
= √156
= 12.49
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(60°))
= arcsin(1.121·0.866)
= 76.12°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(60°))
= arcsin(0.8006·0.866)
= 43.89°
Периметр:
P = a + b + c
= 12.49 + 14 + 10
= 36.49
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√18.25·(18.25-12.49)·(18.25-14)·(18.25-10)
=√18.25 · 5.76 · 4.25 · 8.25
=√3685.77
= 60.71
Высота :
ha =
=
= 9.721
hb =
=
= 8.673
hc =
=
= 12.14