В треугольнике со сторонами: a = 3500, b = 3000, с = 982.9 высоты равны ha = 776.86, hb = 906.34, hc = 2766.3
Ответ:
a=3500
b=3000
c=982.9
α°=112.78°
β°=52.17°
γ°=15°
S = 1359507
ha=776.86
hb=906.34
hc=2766.3
P = 7482.9
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √35002 + 30002 - 2·3500·3000·cos(15°)
= √12250000 + 9000000 - 21000000·0.9659
= √966100
= 982.9
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
3500
982.9
sin(15°))
= arcsin(3.561·0.2588)
= 67.16°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
30002+982.92-35002
2·3000·982.9
)
= arccos(
9000000+966092.41-12250000
5897400
)
= 112.78°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
3000
982.9
sin(15°))
= arcsin(3.052·0.2588)
= 52.17°
Периметр:
P = a + b + c
= 3500 + 3000 + 982.9
= 7482.9
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3741.5·(3741.5-3500)·(3741.5-3000)·(3741.5-982.9)
=√3741.5 · 241.5 · 741.5 · 2758.6
=√1848258754162.3
= 1359507
Высота :
ha =
2S
a
=
2 · 1359507
3500
= 776.86
hb =
2S
b
=
2 · 1359507
3000
= 906.34
hc =
2S
c
=
2 · 1359507
982.9
= 2766.3