В треугольнике со сторонами: a = 5.7, b = 5.7, с = 8.061, углы равны α° = 45°, β° = 45°, γ° = 90°
Ответ:
a=5.7
b=5.7
c=8.061
α°=45°
β°=45°
γ°=90°
S = 16.25
ha=5.702
hb=5.702
hc=4.032
P = 19.46
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5.72 + 5.72 - 2·5.7·5.7·cos(90°)
= √32.49 + 32.49 - 64.98·0
= √64.98
= 8.061
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
5.7
8.061
sin(90°))
= arcsin(0.7071·1)
= 45°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5.72+8.0612-5.72
2·5.7·8.061
)
= arccos(
32.49+64.979721-32.49
91.9
)
= 45°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5.7
8.061
sin(90°))
= arcsin(0.7071·1)
= 45°
Периметр:
P = a + b + c
= 5.7 + 5.7 + 8.061
= 19.46
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√9.731·(9.731-5.7)·(9.731-5.7)·(9.731-8.061)
=√9.731 · 4.031 · 4.031 · 1.67
=√264.05812794997
= 16.25
Высота :
ha =
2S
a
=
2 · 16.25
5.7
= 5.702
hb =
2S
b
=
2 · 16.25
5.7
= 5.702
hc =
2S
c
=
2 · 16.25
8.061
= 4.032