В треугольнике со сторонами: a = 4.2, b = 4.2, с = 2.8, углы равны α° = 70.53°, β° = 70.53°, γ° = 38.94°
Ответ:
a=4.2
b=4.2
c=2.8
α°=70.53°
β°=70.53°
γ°=38.94°
S = 5.544
ha=2.64
hb=2.64
hc=3.96
P = 11.2
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
4.22+2.82-4.22
2·4.2·2.8
)
= arccos(
17.64+7.84-17.64
23.52
)
= 70.53°
Периметр:
P = a + b + c
= 4.2 + 4.2 + 2.8
= 11.2
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.6·(5.6-4.2)·(5.6-4.2)·(5.6-2.8)
=√5.6 · 1.4 · 1.4 · 2.8
=√30.7328
= 5.544
Высота :
ha =
2S
a
=
2 · 5.544
4.2
= 2.64
hb =
2S
b
=
2 · 5.544
4.2
= 2.64
hc =
2S
c
=
2 · 5.544
2.8
= 3.96
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
4.2
4.2
sin(70.53°))
= arcsin(1·0.9428)
= 70.53°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
2.8
4.2
sin(70.53°))
= arcsin(0.6667·0.9428)
= 38.94°