В треугольнике со сторонами: a = 3.002, b = 3.002, с = 3.002, углы равны α° = 59.99°, β° = 59.99°, γ° = 59.99°
Ответ:
a=3.002
b=3.002
c=3.002
α°=59.99°
β°=59.99°
γ°=59.99°
S = 3.902
ha=2.6
hb=2.6
hc=2.6
P = 9.006
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
3.0022+3.0022-3.0022
2·3.002·3.002
)
= arccos(
9.012004+9.012004-9.012004
18.02
)
= 59.99°
Периметр:
P = a + b + c
= 3.002 + 3.002 + 3.002
= 9.006
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√4.503·(4.503-3.002)·(4.503-3.002)·(4.503-3.002)
=√4.503 · 1.501 · 1.501 · 1.501
=√15.228040518003
= 3.902
Высота :
ha =
2S
a
=
2 · 3.902
3.002
= 2.6
hb =
2S
b
=
2 · 3.902
3.002
= 2.6
hc =
2S
c
=
2 · 3.902
3.002
= 2.6
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
3.002
3.002
sin(59.99°))
= arcsin(1·0.8659)
= 59.99°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
3.002
3.002
sin(59.99°))
= arcsin(1·0.8659)
= 59.99°