Решение:
Угол:
α° = arccos(
)
= arccos(
30002+42422-30002
2·3000·4242
)
= arccos(
9000000+17994564-9000000
25452000
)
= 45.01°
Периметр:
P = a + b + c
= 3000 + 3000 + 4242
= 10242
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√5121·(5121-3000)·(5121-3000)·(5121-4242)
=√5121 · 2121 · 2121 · 879
=√20249998153119
= 4500000
Высота :
ha =
=
= 3000
hb =
=
= 3000
hc =
=
= 2121.6
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(45.01°))
= arcsin(1·0.7072)
= 45.01°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(45.01°))
= arcsin(1.414·0.7072)
= 89.64°