В треугольнике со сторонами: a = 11.35, b = 11.35, с = 19.66, углы равны α° = 29.99°, β° = 30°, γ° = 120°
Ответ:
a=11.35
b=11.35
c=19.66
α°=29.99°
β°=30°
γ°=120°
S = 55.77
ha=9.827
hb=9.827
hc=5.673
P = 42.36
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √11.352 + 11.352 - 2·11.35·11.35·cos(120°)
= √128.82 + 128.82 - 257.65·-0.5
= √386.47
= 19.66
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
11.35
19.66
sin(120°))
= arcsin(0.5773·0.866)
= 30°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
11.352+19.662-11.352
2·11.35·19.66
)
= arccos(
128.8225+386.5156-128.8225
446.28
)
= 29.99°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
11.35
19.66
sin(120°))
= arcsin(0.5773·0.866)
= 30°
Периметр:
P = a + b + c
= 11.35 + 11.35 + 19.66
= 42.36
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√21.18·(21.18-11.35)·(21.18-11.35)·(21.18-19.66)
=√21.18 · 9.83 · 9.83 · 1.52
=√3110.83215504
= 55.77
Высота :
ha =
2S
a
=
2 · 55.77
11.35
= 9.827
hb =
2S
b
=
2 · 55.77
11.35
= 9.827
hc =
2S
c
=
2 · 55.77
19.66
= 5.673