В треугольнике со сторонами: a = 9.539392014169456, b = 16.4, с = 8.660254037844386, углы равны α° = 27°, β° = 128.66°, γ° = 24.34°
Ответ:
a=9.539392014169456
b=16.4
c=8.660254037844386
α°=27°
β°=128.66°
γ°=24.34°
S = 32.31
ha=6.774
hb=3.94
hc=7.449
P = 34.6
Решение:
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
8.660254037844386
9.539392014169456
sin(27°))
= arcsin(0.9078·0.454)
= 24.34°
Угол:
β° = 180 - γ° - α°
= 180 - 24.34° - 27°
= 128.66°
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √9.5393920141694562 + 8.6602540378443862 - 2·9.539392014169456·8.660254037844386·cos(128.66°)
= √91 + 75 - 165.23·-0.6247
= √269.22
= 16.41
или:
b = a·
sin(β°)
sin(α°)
= 9.539392014169456·
sin(128.66°)
sin(27°)
= 9.539392014169456·
0.7809
0.454
= 9.539392014169456·1.72
= 16.41
или:
b = c·
sin(β°)
sin(γ°)
= 8.660254037844386·
sin(128.66°)
sin(24.34°)
= 8.660254037844386·
0.7809
0.4122
= 8.660254037844386·1.894
= 16.4
Высота :
hc = a·sin(β°)
= 9.539392014169456·sin(128.66°)
= 9.539392014169456·0.7809
= 7.449
Периметр:
P = a + b + c
= 9.539392014169456 + 16.4 + 8.660254037844386
= 34.6
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√17.3·(17.3-9.539392014169456)·(17.3-16.4)·(17.3-8.660254037844386)
=√17.3 · 7.7606079858305 · 0.9 · 8.6397459621556
=√1043.9635411022
= 32.31
Высота :
ha =
2S
a
=
2 · 32.31
9.539392014169456
= 6.774
hb =
2S
b
=
2 · 32.31
16.4
= 3.94