В треугольнике со сторонами: a = 9.482, b = 5, с = 9.8 высоты равны ha = 1.4, hb = 9.288, hc = 4.739
Ответ:
a=9.482
b=5
c=9.8
α°=71.48°
β°=30°
γ°=78.52°
S = 23.22
ha=1.4
hb=9.288
hc=4.739
P = 24.28
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
9.8
5
sin(30°))
= arcsin(1.96·0.5)
= 78.52°
Угол:
α° = 180 - γ° - β°
= 180 - 78.52° - 30°
= 71.48°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √52 + 9.82 - 2·5·9.8·cos(71.48°)
= √25 + 96.04 - 98·0.3176
= √89.92
= 9.483
или:
a = b·
sin(α°)
sin(β°)
= 5·
sin(71.48°)
sin(30°)
= 5·
0.9482
0.5
= 5·1.896
= 9.48
или:
a = c·
sin(α°)
sin(γ°)
= 9.8·
sin(71.48°)
sin(78.52°)
= 9.8·
0.9482
0.98
= 9.8·0.9676
= 9.482
Периметр:
P = a + b + c
= 9.482 + 5 + 9.8
= 24.28
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√12.14·(12.14-9.482)·(12.14-5)·(12.14-9.8)
=√12.14 · 2.658 · 7.14 · 2.34
=√539.122841712
= 23.22
hb =
2S
b
=
2 · 23.22
5
= 9.288
hc =
2S
c
=
2 · 23.22
9.8
= 4.739