В треугольнике со сторонами: a = 0.2, b = 0.2, с = 0.1035, углы равны α° = 75°, β° = 75.02°, γ° = 30°
Ответ:
a=0.2
b=0.2
c=0.1035
α°=75°
β°=75.02°
γ°=30°
S = 0.01001
ha=0.1001
hb=0.1001
hc=0.1934
P = 0.5035
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √0.22 + 0.22 - 2·0.2·0.2·cos(30°)
= √0.04 + 0.04 - 0.08·0.866
= √0.01072
= 0.1035
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
0.2
0.1035
sin(30°))
= arcsin(1.932·0.5)
= 75.02°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
0.22+0.10352-0.22
2·0.2·0.1035
)
= arccos(
0.04+0.01071225-0.04
0.0414
)
= 75°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
0.2
0.1035
sin(30°))
= arcsin(1.932·0.5)
= 75.02°
Периметр:
P = a + b + c
= 0.2 + 0.2 + 0.1035
= 0.5035
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√0.2518·(0.2518-0.2)·(0.2518-0.2)·(0.2518-0.1035)
=√0.2518 · 0.0518 · 0.0518 · 0.1483
=√0.0001001973870856
= 0.01001
Высота :
ha =
2S
a
=
2 · 0.01001
0.2
= 0.1001
hb =
2S
b
=
2 · 0.01001
0.2
= 0.1001
hc =
2S
c
=
2 · 0.01001
0.1035
= 0.1934