В треугольнике со сторонами: a = 16.73, b = 20, с = 16, углы равны α° = 54°, β° = 75.18°, γ° = 50.69°
Ответ:
a=16.73
b=20
c=16
α°=54°
β°=75.18°
γ°=50.69°
S = 129.58
ha=15.49
hb=12.96
hc=16.2
P = 52.73
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √202 + 162 - 2·20·16·cos(54°)
= √400 + 256 - 640·0.5878
= √279.81
= 16.73
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
20
16.73
sin(54°))
= arcsin(1.195·0.809)
= 75.18°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
16
16.73
sin(54°))
= arcsin(0.9564·0.809)
= 50.69°
Периметр:
P = a + b + c
= 16.73 + 20 + 16
= 52.73
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√26.37·(26.37-16.73)·(26.37-20)·(26.37-16)
=√26.37 · 9.64 · 6.37 · 10.37
=√16792.11316692
= 129.58
Высота :
ha =
2S
a
=
2 · 129.58
16.73
= 15.49
hb =
2S
b
=
2 · 129.58
20
= 12.96
hc =
2S
c
=
2 · 129.58
16
= 16.2