В треугольнике со сторонами: a = 80, b = 80, с = 61.23 высоты равны ha = 56.58, hb = 56.58, hc = 73.93
Ответ:
a=80
b=80
c=61.23
α°=67.5°
β°=67.54°
γ°=45°
S = 2263.3
ha=56.58
hb=56.58
hc=73.93
P = 221.23
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √802 + 802 - 2·80·80·cos(45°)
= √6400 + 6400 - 12800·0.7071
= √3749.1
= 61.23
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
80
61.23
sin(45°))
= arcsin(1.307·0.7071)
= 67.54°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
802+61.232-802
2·80·61.23
)
= arccos(
6400+3749.1129-6400
9796.8
)
= 67.5°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
80
61.23
sin(45°))
= arcsin(1.307·0.7071)
= 67.54°
Периметр:
P = a + b + c
= 80 + 80 + 61.23
= 221.23
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√110.62·(110.62-80)·(110.62-80)·(110.62-61.23)
=√110.62 · 30.62 · 30.62 · 49.39
=√5122512.8087399
= 2263.3
Высота :
ha =
2S
a
=
2 · 2263.3
80
= 56.58
hb =
2S
b
=
2 · 2263.3
80
= 56.58
hc =
2S
c
=
2 · 2263.3
61.23
= 73.93