В треугольнике со сторонами: a = 35.8, b = 20.6, с = 41.92, углы равны α° = 58.59°, β° = 29.41°, γ° = 92°
Ответ:
a=35.8
b=20.6
c=41.92
α°=58.59°
β°=29.41°
γ°=92°
S = 368.52
ha=20.59
hb=35.78
hc=17.58
P = 98.32
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √35.82 + 20.62 - 2·35.8·20.6·cos(92°)
= √1281.6 + 424.36 - 1475·-0.0349
= √1757.4
= 41.92
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
35.8
41.92
sin(92°))
= arcsin(0.854·0.9994)
= 58.59°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
20.62+41.922-35.82
2·20.6·41.92
)
= arccos(
424.36+1757.2864-1281.64
1727.1
)
= 58.59°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
20.6
41.92
sin(92°))
= arcsin(0.4914·0.9994)
= 29.41°
Периметр:
P = a + b + c
= 35.8 + 20.6 + 41.92
= 98.32
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√49.16·(49.16-35.8)·(49.16-20.6)·(49.16-41.92)
=√49.16 · 13.36 · 28.56 · 7.24
=√135804.79417344
= 368.52
Высота :
ha =
2S
a
=
2 · 368.52
35.8
= 20.59
hb =
2S
b
=
2 · 368.52
20.6
= 35.78
hc =
2S
c
=
2 · 368.52
41.92
= 17.58