В треугольнике со сторонами: a = 115.56, b = 116, с = 19.17 высоты равны ha = 19.15, hb = 19.07, hc = 115.42
Ответ:
a=115.56
b=116
c=19.17
α°=83.94°
β°=86.77°
γ°=9.5°
S = 1106.3
ha=19.15
hb=19.07
hc=115.42
P = 250.73
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √115.562 + 1162 - 2·115.56·116·cos(9.5°)
= √13354.1 + 13456 - 26809.9·0.9863
= √367.5
= 19.17
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
115.56
19.17
sin(9.5°))
= arcsin(6.028·0.165)
= 84.05°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
1162+19.172-115.562
2·116·19.17
)
= arccos(
13456+367.4889-13354.1136
4447.4
)
= 83.94°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
116
19.17
sin(9.5°))
= arcsin(6.051·0.165)
= 86.77°
Периметр:
P = a + b + c
= 115.56 + 116 + 19.17
= 250.73
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√125.37·(125.37-115.56)·(125.37-116)·(125.37-19.17)
=√125.37 · 9.81 · 9.37 · 106.2
=√1223845.9101918
= 1106.3
Высота :
ha =
2S
a
=
2 · 1106.3
115.56
= 19.15
hb =
2S
b
=
2 · 1106.3
116
= 19.07
hc =
2S
c
=
2 · 1106.3
19.17
= 115.42