Решение:
Угол:
α° = arccos(
)
= arccos(
602+69.9714232-362
2·60·69.971423
)
= arccos(
3600+4896.0000366449-1296
8396.6
)
= 30.96°
Периметр:
P = a + b + c
= 36 + 60 + 69.971423
= 165.97
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√82.99·(82.99-36)·(82.99-60)·(82.99-69.971423)
=√82.99 · 46.99 · 22.99 · 13.018577
=√1167168.8732011
= 1080.4
Высота :
ha =
=
= 60.02
hb =
=
= 36.01
hc =
=
= 30.88
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(30.96°))
= arcsin(1.667·0.5144)
= 59.04°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(30.96°))
= arcsin(1.944·0.5144)
= 89.8°