В треугольнике со сторонами: a = 359.3, b = 578.73, с = 509, углы равны α° = 37.9°, β° = 81.62°, γ° = 60.48°
Ответ:
a=359.3
b=578.73
c=509
α°=37.9°
β°=81.62°
γ°=60.48°
S = 90471.2
ha=503.6
hb=312.65
hc=355.49
P = 1447
Решение:
Сторона:
b = c·
sin(β°)
sin(γ°)
= 509·
sin(81.62°)
sin(60.48°)
= 509·
0.9893
0.8702
= 509·1.137
= 578.73
Угол:
α° = 180 - γ° - β°
= 180 - 60.48° - 81.62°
= 37.9°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √578.732 + 5092 - 2·578.73·509·cos(37.9°)
= √334928.4 + 259081 - 589147.1·0.7891
= √129113.4
= 359.32
или:
a = b·
sin(α°)
sin(β°)
= 578.73·
sin(37.9°)
sin(81.62°)
= 578.73·
0.6143
0.9893
= 578.73·0.6209
= 359.33
или:
a = c·
sin(α°)
sin(γ°)
= 509·
sin(37.9°)
sin(60.48°)
= 509·
0.6143
0.8702
= 509·0.7059
= 359.3
Периметр:
P = a + b + c
= 359.3 + 578.73 + 509
= 1447
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√723.52·(723.52-359.3)·(723.52-578.73)·(723.52-509)
=√723.52 · 364.22 · 144.79 · 214.52
=√8185037756.6394
= 90471.2
Высота :
ha =
2S
a
=
2 · 90471.2
359.3
= 503.6
hb =
2S
b
=
2 · 90471.2
578.73
= 312.65
hc =
2S
c
=
2 · 90471.2
509
= 355.49