В треугольнике со сторонами: a = 42.28, b = 42.74, с = 23.4, углы равны α° = 72.94°, β° = 75.13°, γ° = 31.95°
Ответ:
a=42.28
b=42.74
c=23.4
α°=72.94°
β°=75.13°
γ°=31.95°
S = 478.07
ha=22.61
hb=22.37
hc=40.86
P = 108.42
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
42.742+23.42-42.282
2·42.74·23.4
)
= arccos(
1826.7076+547.56-1787.5984
2000.2
)
= 72.94°
Периметр:
P = a + b + c
= 42.28 + 42.74 + 23.4
= 108.42
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√54.21·(54.21-42.28)·(54.21-42.74)·(54.21-23.4)
=√54.21 · 11.93 · 11.47 · 30.81
=√228546.70647471
= 478.07
Высота :
ha =
2S
a
=
2 · 478.07
42.28
= 22.61
hb =
2S
b
=
2 · 478.07
42.74
= 22.37
hc =
2S
c
=
2 · 478.07
23.4
= 40.86
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
42.74
42.28
sin(72.94°))
= arcsin(1.011·0.956)
= 75.13°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
23.4
42.28
sin(72.94°))
= arcsin(0.5535·0.956)
= 31.95°