В треугольнике со сторонами: a = 13.85, b = 13.85, с = 23.99, углы равны α° = 30°, β° = 30°, γ° = 120°
Ответ:
a=13.85
b=13.85
c=23.99
α°=30°
β°=30°
γ°=120°
S = 83.21
ha=12.02
hb=12.02
hc=6.937
P = 51.69
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √13.852 + 13.852 - 2·13.85·13.85·cos(120°)
= √191.82 + 191.82 - 383.65·-0.5
= √575.47
= 23.99
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
13.85
23.99
sin(120°))
= arcsin(0.5773·0.866)
= 30°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
13.852+23.992-13.852
2·13.85·23.99
)
= arccos(
191.8225+575.5201-191.8225
664.52
)
= 30°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
13.85
23.99
sin(120°))
= arcsin(0.5773·0.866)
= 30°
Периметр:
P = a + b + c
= 13.85 + 13.85 + 23.99
= 51.69
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√25.85·(25.85-13.85)·(25.85-13.85)·(25.85-23.99)
=√25.85 · 12 · 12 · 1.86
=√6923.664
= 83.21
Высота :
ha =
2S
a
=
2 · 83.21
13.85
= 12.02
hb =
2S
b
=
2 · 83.21
13.85
= 12.02
hc =
2S
c
=
2 · 83.21
23.99
= 6.937