В треугольнике со сторонами: a = 3.61, b = 3.61, с = 3.61, углы равны α° = 59.99°, β° = 59.99°, γ° = 59.99°
Ответ:
a=3.61
b=3.61
c=3.61
α°=59.99°
β°=59.99°
γ°=59.99°
S = 5.643
ha=3.126
hb=3.126
hc=3.126
P = 10.83
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
3.612+3.612-3.612
2·3.61·3.61
)
= arccos(
13.0321+13.0321-13.0321
26.06
)
= 59.99°
Периметр:
P = a + b + c
= 3.61 + 3.61 + 3.61
= 10.83
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.415·(5.415-3.61)·(5.415-3.61)·(5.415-3.61)
=√5.415 · 1.805 · 1.805 · 1.805
=√31.844180701875
= 5.643
Высота :
ha =
2S
a
=
2 · 5.643
3.61
= 3.126
hb =
2S
b
=
2 · 5.643
3.61
= 3.126
hc =
2S
c
=
2 · 5.643
3.61
= 3.126
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
3.61
3.61
sin(59.99°))
= arcsin(1·0.8659)
= 59.99°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
3.61
3.61
sin(59.99°))
= arcsin(1·0.8659)
= 59.99°