В треугольнике со сторонами: a = 7.26, b = 7.68, с = 6.5, углы равны α° = 60.92°, β° = 67.61°, γ° = 51.48°
Ответ:
a=7.26
b=7.68
c=6.5
α°=60.92°
β°=67.61°
γ°=51.48°
S = 21.81
ha=6.008
hb=5.68
hc=6.711
P = 21.44
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
7.682+6.52-7.262
2·7.68·6.5
)
= arccos(
58.9824+42.25-52.7076
99.84
)
= 60.92°
Периметр:
P = a + b + c
= 7.26 + 7.68 + 6.5
= 21.44
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.72·(10.72-7.26)·(10.72-7.68)·(10.72-6.5)
=√10.72 · 3.46 · 3.04 · 4.22
=√475.83558656
= 21.81
Высота :
ha =
2S
a
=
2 · 21.81
7.26
= 6.008
hb =
2S
b
=
2 · 21.81
7.68
= 5.68
hc =
2S
c
=
2 · 21.81
6.5
= 6.711
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
7.68
7.26
sin(60.92°))
= arcsin(1.058·0.8739)
= 67.61°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
6.5
7.26
sin(60.92°))
= arcsin(0.8953·0.8739)
= 51.48°