В треугольнике со сторонами: a = 482.4, b = 550, с = 400, углы равны α° = 58.53°, β° = 76.47°, γ° = 45°
Ответ:
a=482.4
b=550
c=400
α°=58.53°
β°=76.47°
γ°=45°
S = 93807.1
ha=388.92
hb=341.12
hc=469.04
P = 1432.4
Решение:
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
550
400
sin(45°))
= arcsin(1.375·0.7071)
= 76.47°
Угол:
α° = 180 - γ° - β°
= 180 - 45° - 76.47°
= 58.53°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √5502 + 4002 - 2·550·400·cos(58.53°)
= √302500 + 160000 - 440000·0.5221
= √232776
= 482.47
или:
a = b·
sin(α°)
sin(β°)
= 550·
sin(58.53°)
sin(76.47°)
= 550·
0.8529
0.9722
= 550·0.8773
= 482.52
или:
a = c·
sin(α°)
sin(γ°)
= 400·
sin(58.53°)
sin(45°)
= 400·
0.8529
0.7071
= 400·1.206
= 482.4
Периметр:
P = a + b + c
= 482.4 + 550 + 400
= 1432.4
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√716.2·(716.2-482.4)·(716.2-550)·(716.2-400)
=√716.2 · 233.8 · 166.2 · 316.2
=√8799777850.0464
= 93807.1
Высота :
ha =
2S
a
=
2 · 93807.1
482.4
= 388.92
hb =
2S
b
=
2 · 93807.1
550
= 341.12
hc =
2S
c
=
2 · 93807.1
400
= 469.04