Решение:
Угол:
α° = arccos(
)
= arccos(
26602+25802-14202
2·2660·2580
)
= arccos(
7075600+6656400-2016400
13725600
)
= 31.4°
Периметр:
P = a + b + c
= 1420 + 2660 + 2580
= 6660
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√3330·(3330-1420)·(3330-2660)·(3330-2580)
=√3330 · 1910 · 670 · 750
=√3196050750000
= 1787750
Высота :
ha =
=
= 2518
hb =
=
= 1344.2
hc =
=
= 1385.9
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(31.4°))
= arcsin(1.873·0.521)
= 77.38°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(31.4°))
= arcsin(1.817·0.521)
= 71.2°