В треугольнике со сторонами: a = 12.124355653, b = 5.1961524227, с = 8.6602540378 высоты равны ha = 3.213, hb = 7.498, hc = 4.499
Ответ:
a=12.124355653
b=5.1961524227
c=8.6602540378
α°=120°
β°=21.79°
γ°=38.21°
S = 19.48
ha=3.213
hb=7.498
hc=4.499
P = 25.98
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5.19615242272+8.66025403782-12.1243556532
2·5.1961524227·8.6602540378
)
= arccos(
26.999999999931+74.999999999231-147.00000000043
90
)
= 120°
Периметр:
P = a + b + c
= 12.124355653 + 5.1961524227 + 8.6602540378
= 25.98
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√12.99·(12.99-12.124355653)·(12.99-5.1961524227)·(12.99-8.6602540378)
=√12.99 · 0.865644347 · 7.7938475773 · 4.3297459622
=√379.45735254746
= 19.48
Высота :
ha =
2S
a
=
2 · 19.48
12.124355653
= 3.213
hb =
2S
b
=
2 · 19.48
5.1961524227
= 7.498
hc =
2S
c
=
2 · 19.48
8.6602540378
= 4.499
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
5.1961524227
12.124355653
sin(120°))
= arcsin(0.4286·0.866)
= 21.79°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
8.6602540378
12.124355653
sin(120°))
= arcsin(0.7143·0.866)
= 38.21°