В треугольнике со сторонами: a = 504.14, b = 493.6, с = 85 высоты равны ha = 83.16, hb = 84.93, hc = 493.22
Ответ:
a=504.14
b=493.6
c=85
α°=92.2°
β°=78.1°
γ°=9.7°
S = 20961.9
ha=83.16
hb=84.93
hc=493.22
P = 1082.7
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 92.2° - 78.1°
= 9.7°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 85·
sin(92.2°)
sin(9.7°)
= 85·
0.9993
0.1685
= 85·5.931
= 504.14
Сторона:
b = c·
sin(β°)
sin(γ°)
= 85·
sin(78.1°)
sin(9.7°)
= 85·
0.9785
0.1685
= 85·5.807
= 493.6
Периметр:
P = a + b + c
= 504.14 + 493.6 + 85
= 1082.7
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√541.37·(541.37-504.14)·(541.37-493.6)·(541.37-85)
=√541.37 · 37.23 · 47.77 · 456.37
=√439399492.55253
= 20961.9
Высота :
ha =
2S
a
=
2 · 20961.9
504.14
= 83.16
hb =
2S
b
=
2 · 20961.9
493.6
= 84.93
hc =
2S
c
=
2 · 20961.9
85
= 493.22