Решение:
Угол:
α° = arccos(
)
= arccos(
2.602+2.152-2.402
2·2.60·2.15
)
= arccos(
)
= 59.81°
Периметр:
P = a + b + c
= 2.40 + 2.60 + 2.15
= 7.15
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√3.575·(3.575-2.40)·(3.575-2.60)·(3.575-2.15)
=√3.575 · 1.175 · 0.975 · 1.425
=√5.836243359375
= 2.416
Высота :
ha =
=
= 2.013
hb =
=
= 1.858
hc =
=
= 2.247
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(59.81°))
= arcsin(1.083·0.8644)
= 69.41°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(59.81°))
= arcsin(0.8958·0.8644)
= 50.74°