В треугольнике со сторонами: a = 15.6, b = 23.7, с = 21.5 высоты равны ha = 21, hb = 13.82, hc = 15.24
Ответ:
a=15.6
b=23.7
c=21.5
α°=40.01°
β°=77.57°
γ°=62.36°
S = 163.79
ha=21
hb=13.82
hc=15.24
P = 60.8
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
23.72+21.52-15.62
2·23.7·21.5
)
= arccos(
561.69+462.25-243.36
1019.1
)
= 40.01°
Периметр:
P = a + b + c
= 15.6 + 23.7 + 21.5
= 60.8
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√30.4·(30.4-15.6)·(30.4-23.7)·(30.4-21.5)
=√30.4 · 14.8 · 6.7 · 8.9
=√26828.7296
= 163.79
Высота :
ha =
2S
a
=
2 · 163.79
15.6
= 21
hb =
2S
b
=
2 · 163.79
23.7
= 13.82
hc =
2S
c
=
2 · 163.79
21.5
= 15.24
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
23.7
15.6
sin(40.01°))
= arcsin(1.519·0.6429)
= 77.57°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
21.5
15.6
sin(40.01°))
= arcsin(1.378·0.6429)
= 62.36°