В треугольнике со сторонами: a = 13.78, b = 5, с = 9.8 высоты равны ha = 1.4, hb = 6.976, hc = 3.559
Ответ:
a=13.78
b=5
c=9.8
α°=134.52°
β°=15°
γ°=30.48°
S = 17.44
ha=1.4
hb=6.976
hc=3.559
P = 28.58
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
9.8
5
sin(15°))
= arcsin(1.96·0.2588)
= 30.48°
Угол:
α° = 180 - γ° - β°
= 180 - 30.48° - 15°
= 134.52°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √52 + 9.82 - 2·5·9.8·cos(134.52°)
= √25 + 96.04 - 98·-0.7012
= √189.76
= 13.78
или:
a = b·
sin(α°)
sin(β°)
= 5·
sin(134.52°)
sin(15°)
= 5·
0.713
0.2588
= 5·2.755
= 13.78
или:
a = c·
sin(α°)
sin(γ°)
= 9.8·
sin(134.52°)
sin(30.48°)
= 9.8·
0.713
0.5072
= 9.8·1.406
= 13.78
Периметр:
P = a + b + c
= 13.78 + 5 + 9.8
= 28.58
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√14.29·(14.29-13.78)·(14.29-5)·(14.29-9.8)
=√14.29 · 0.51 · 9.29 · 4.49
=√303.99361359
= 17.44
hb =
2S
b
=
2 · 17.44
5
= 6.976
hc =
2S
c
=
2 · 17.44
9.8
= 3.559