В треугольнике со сторонами: a = 52.9, b = 42.5, с = 63.4 высоты равны ha = 42.14, hb = 52.45, hc = 35.16
Ответ:
a=52.9
b=42.5
c=63.4
α°=55.82°
β°=41.66°
γ°=82.35°
S = 1114.6
ha=42.14
hb=52.45
hc=35.16
P = 158.8
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
42.52+63.42-52.92
2·42.5·63.4
)
= arccos(
1806.25+4019.56-2798.41
5389
)
= 55.82°
Периметр:
P = a + b + c
= 52.9 + 42.5 + 63.4
= 158.8
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√79.4·(79.4-52.9)·(79.4-42.5)·(79.4-63.4)
=√79.4 · 26.5 · 36.9 · 16
=√1242260.64
= 1114.6
Высота :
ha =
2S
a
=
2 · 1114.6
52.9
= 42.14
hb =
2S
b
=
2 · 1114.6
42.5
= 52.45
hc =
2S
c
=
2 · 1114.6
63.4
= 35.16
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
42.5
52.9
sin(55.82°))
= arcsin(0.8034·0.8273)
= 41.66°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
63.4
52.9
sin(55.82°))
= arcsin(1.198·0.8273)
= 82.35°