В треугольнике со сторонами: a = 5, b = 3, с = 4.36 высоты равны ha = 2.599, hb = 4.331, hc = 2.98
Ответ:
a=5
b=3
c=4.36
α°=83.39°
β°=36.58°
γ°=60°
S = 6.497
ha=2.599
hb=4.331
hc=2.98
P = 12.36
Решение:
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
5
4.36
sin(60°))
= arcsin(1.147·0.866)
= 83.36°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
32+4.362-52
2·3·4.36
)
= arccos(
9+19.0096-25
26.16
)
= 83.39°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
3
4.36
sin(60°))
= arcsin(0.6881·0.866)
= 36.58°
Периметр:
P = a + b + c
= 5 + 3 + 4.36
= 12.36
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√6.18·(6.18-5)·(6.18-3)·(6.18-4.36)
=√6.18 · 1.18 · 3.18 · 1.82
=√42.20549424
= 6.497
Высота :
ha =
2S
a
=
2 · 6.497
5
= 2.599
hb =
2S
b
=
2 · 6.497
3
= 4.331
hc =
2S
c
=
2 · 6.497
4.36
= 2.98