В треугольнике со сторонами: a = 6.5, b = 4.806, с = 6, углы равны α° = 73.01°, β° = 45°, γ° = 61.94°
Ответ:
a=6.5
b=4.806
c=6
α°=73.01°
β°=45°
γ°=61.94°
S = 13.79
ha=4.243
hb=5.739
hc=4.596
P = 17.31
Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √6.52 + 62 - 2·6.5·6·cos(45°)
= √42.25 + 36 - 78·0.7071
= √23.1
= 4.806
Высота :
hc = a·sin(β°)
= 6.5·sin(45°)
= 6.5·0.7071
= 4.596
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
6.5
4.806
sin(45°))
= arcsin(1.352·0.7071)
= 72.94°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
4.8062+62-6.52
2·4.806·6
)
= arccos(
23.097636+36-42.25
57.67
)
= 73.01°
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
6
4.806
sin(45°))
= arcsin(1.248·0.7071)
= 61.94°
Периметр:
P = a + b + c
= 6.5 + 4.806 + 6
= 17.31
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√8.653·(8.653-6.5)·(8.653-4.806)·(8.653-6)
=√8.653 · 2.153 · 3.847 · 2.653
=√190.13854657572
= 13.79
Высота :
ha =
2S
a
=
2 · 13.79
6.5
= 4.243
hb =
2S
b
=
2 · 13.79
4.806
= 5.739