В треугольнике со сторонами: a = 42.28, b = 42.74, с = 20.6, углы равны α° = 74.74°, β° = 77.24°, γ° = 28.03°
Ответ:
a=42.28
b=42.74
c=20.6
α°=74.74°
β°=77.24°
γ°=28.03°
S = 424.7
ha=20.09
hb=19.87
hc=41.23
P = 105.62
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
42.742+20.62-42.282
2·42.74·20.6
)
= arccos(
1826.7076+424.36-1787.5984
1760.9
)
= 74.74°
Периметр:
P = a + b + c
= 42.28 + 42.74 + 20.6
= 105.62
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√52.81·(52.81-42.28)·(52.81-42.74)·(52.81-20.6)
=√52.81 · 10.53 · 10.07 · 32.21
=√180370.17807471
= 424.7
Высота :
ha =
2S
a
=
2 · 424.7
42.28
= 20.09
hb =
2S
b
=
2 · 424.7
42.74
= 19.87
hc =
2S
c
=
2 · 424.7
20.6
= 41.23
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
42.74
42.28
sin(74.74°))
= arcsin(1.011·0.9647)
= 77.24°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
20.6
42.28
sin(74.74°))
= arcsin(0.4872·0.9647)
= 28.03°