В треугольнике со сторонами: a = 509.15, b = 498.61, с = 85 высоты равны ha = 83.17, hb = 84.93, hc = 498.21
Ответ:
a=509.15
b=498.61
c=85
α°=92.3°
β°=78.1°
γ°=9.6°
S = 21173.9
ha=83.17
hb=84.93
hc=498.21
P = 1092.8
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 92.3° - 78.1°
= 9.6°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 85·
sin(92.3°)
sin(9.6°)
= 85·
0.9992
0.1668
= 85·5.99
= 509.15
Сторона:
b = c·
sin(β°)
sin(γ°)
= 85·
sin(78.1°)
sin(9.6°)
= 85·
0.9785
0.1668
= 85·5.866
= 498.61
Периметр:
P = a + b + c
= 509.15 + 498.61 + 85
= 1092.8
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√546.38·(546.38-509.15)·(546.38-498.61)·(546.38-85)
=√546.38 · 37.23 · 47.77 · 461.38
=√448334165.79178
= 21173.9
Высота :
ha =
2S
a
=
2 · 21173.9
509.15
= 83.17
hb =
2S
b
=
2 · 21173.9
498.61
= 84.93
hc =
2S
c
=
2 · 21173.9
85
= 498.21