Решение:
Угол:
α° = arccos(
)
= arccos(
)
= arccos(
)
= 58.43°
Периметр:
P = a + b + c
= 164 + 169 + 167
= 500
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√250·(250-164)·(250-169)·(250-167)
=√250 · 86 · 81 · 83
=√144544500
= 12022.7
hb =
=
= 142.28
hc =
=
= 143.98
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(58.43°))
= arcsin(1.03·0.852)
= 61.35°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(58.43°))
= arcsin(1.018·0.852)
= 60.15°